Nobel de Física a investigadores de la “ruptura espontánea de la simetría”

■ El sobrante después del Big Bang, origen de toda la materia del universo, postulan

■ Descubrieron la tercera generación de quarks (top) para completar el Modelo estándar

Afp y Dpa

Yoichiro Nambu

Estocolmo, 7 de octubre. El Premio Nobel de Física 2008 fue atribuido al estadunidense Yoichiro Nambu y a los japoneses Makoto Kobayashi y Toshihide Maskawa por trabajos separados sobre la física y las partículas elementales de la materia, llamadas quarks, anunció el martes el Comité Nobel.

Nambu, de 87 años, nacido en 1921 en Japón y que trabajaba en el Instituto Enrico Fermi de Chicago, recibirá la mitad del premio por el descubrimiento del mecanismo de la “ruptura espontánea de simetría en física subatómica”, según los considerandos del Comité Nobel.

Sus trabajos alimentan la teoría del Modelo estándar, que trata de describir las partículas elementales que ayudan a explicar la naturaleza de la materia y los orígenes del universo, creado en el Big Bang, hace unos 14 mil millones de años.

Los dos científicos japoneses fueron galardonados “por el descubrimiento del origen de la ruptura espontánea de simetría que supone la existencia de por lo menos tres familias de quarks en la naturaleza”, agregó el comité.

Kobayashi, de 64 años, es profesor honorario del centro de investigaciones de Tsukuba. Maskawa, de 68 años, es profesor honorario en el Instituto de Física Teórica de Yukawa (ambos en Japón).

Explicación fundamental



Makoto Kobayashi

El Premio Nobel de Física 2008 fue otorgado por una explicación fundamental sobre la existencia de la humanidad: si las leyes de la naturaleza fueran perfectamente simétricas, no habría seres humanos, no habría Tierra, no habría estrellas. En realidad, el Universo carecería de materia.

La materia y antimateria se hubiesen anulado mutuamente después de la explosión inicial, el Big Bang. Por la investigación de las rupturas de simetría de la naturaleza, que entre otros permitieron la “supervivencia” de un pequeño sobrante de materia, el físico estadunidense Yoichiro Nambu comparte con sus colegas japoneses Makoto Kobayashi y Toshihide Maskawa el mayor premio de su disciplina.

Una ruptura de simetría semejante hizo posible que tras el Big Bang sobrara una única partícula de materia por cada 10 mil millones de partículas de antimateria.

“Este sobrante de materia fue la siembra de todo nuestro universo, que se llenó de galaxias, estrella y planetas, y por último de vida”. Con estas palabras explicó hoy el Comité Nobel en Estocolmo la importancia fundamental de los trabajos premiados.

La ruptura de simetría que generó materia después del Big Bang es un hecho que aún no se comprende en su totalidad. Sin embargo, este tipo de rupturas de simetría tienen un papel también en otros ámbitos de la naturaleza.

Los físicos observaron este fenómeno en sus laboratorios ya en los años 60, pero no lo podían explicar. Kobayashi y Maskawa reconocieron en 1972 en la Universidad de Kyoto que las rupturas de simetría se podrían integrar a la teoría vigente, en el caso de que existiera entre las partículas elementales, una tercera generación aún no descubierta de quarks.

Los quarks son los componentes más pequeños de los núcleos atómicos. En 1977 se halló el quark bottom y en 1994 finalmente el top, el tercer par de quarks de la naturaleza.

Con la tercera generación de quarks descrita por los dos físicos japoneses se pudieron integrar las rupturas de simetría al Modelo estándar, explicó Andrzej Jerzy Buras del Instituto de Física Teórica de la Universidad Técnica de Munich, Alemania. “Eso funciona de manera fantá

El Modelo estándar de nuestro mundo reúne las partículas elementales y tres de las cuatro fuerzas fundamentales de la naturaleza, sólo queda por el momento excluida la gravedad.

También funciona bien, porque Yoichiro Nambu formuló la descripción matemática de las rupturas espontáneas de simetría en el mundo de las partículas elementales, que atraviesan en la actualidad del Modelo estándar.

“Las rupturas espontáneas de simetría esconden el orden de la naturaleza debajo de una superficie desordenada”, explicó el Comité Nobel, e ilustró esto con el ejemplo de un lápiz, que está parado sobre uno de sus extremos: en cuanto cae se rompe la simetría y el orden se destruye.

“Nambu tuvo las extraordinarias ideas básicas. Los otros dos se encargaron luego de un problema irresoluto”, dijo Lars Brink, del Comité Nobel.

Los trabajos de Kobayashi y Maskawa, sin embargo, no pueden explicar por qué después del Big Bang sobró algo de materia.

La respuesta a esta pregunta la esperan obtener los científicos del nuevo acelerador de partículas, el gran colisionador de hadrones (LHC, por sus siglas en inglés), del Consejo Europeo para la Investigación Nuclear (CERN) en Ginebra.

Con este aparato de investigación, el más grande jamás construido por el hombre, los físicos esperan acercarse a las condiciones reinantes durante la explosión inicial y resolver de esta manera el enigma alrededor de nuestra existencia.



Toshihide Maskawa

Silencio

El anuncio de los ganadores del Premio Nobel de Física 2008 dejó hoy a algunos sin habla. Al galardonado japonés Makoto Kobayashi, por ejemplo, al ser llamado por la Real Academia Sueca de Ciencias de Estocolmo no se le ocurrió nada que decir sobre el otorgamiento del premio.

“¿Cuál fue su reacción cuando recibió la noticia?”, le preguntaron al físico por teléfono. Su respuesta: silencio. Sólo después de que una comprensiva periodista consultó: “¿Está usted tal vez en estado de shock?, se escuchó un tímido “sí”.

También los periodistas reunidos en la Real Academia Sueca de Ciencias estaban en silencio. Simplemente, no se les ocurría ninguna pregunta relacionada con los complicados problemas de la física teórica, por cuya solución Kobayashi, su colega Toshihide Maskawa, así como el maestro de Kobayashi emigrado a Estados Unidos, Yoichiro Nambu, fueron distinguidos hoy con el prestigioso galardón.

Con asombro, los representantes de los medios escucharon el apasionado discurso del físico sueco y miembro del Comité Nobel, Lars Brink, acerca de los logros de los tres premiados.

Este miembro del jurado movió constantemente de aquí para allá durante su discurso ante los cerca de 50 periodistas una manzana, cuya forma no del todo simétrica ilustra muy bien, según explicó, los descubrimientos de Nambu sobre la ruptura de simetrías.

Cuando Brink terminó su exposición y abrió espacio para las preguntas, todos los presentes cayeron en un largo silencio.

Nadie quería, aparentemente, romper el delgado hielo de la física teórica de partículas.

Un miembro del comité de prensa de la Academia de Ciencias se compadeció finalmente del jurado, que miraba decepcionado, y formuló una sencilla pregunta, que, según dijo explícitamente, era “para romper el hielo”.

A ella siguieron nuevas explicaciones de Brink sobre las teorías de la explosión inicial. Aquí, un periodista de Estocolmo vio la oportunidad para engancharse: “¿Qué pasaría si la ruptura espontánea de simetría descubierta por Nambu no existiera?”

La respuesta de Brink: “Entonces no estaríamos hoy aquí sentados, ni usted ni yo”. Insiste: “Pero sí estaríamos aquí sentados, ¿sólo en otra versión?” Respuesta: “Sí, exactamente”.

Luego de que Kobayashi guardó silencio en el teléfono ante las preguntas de los periodistas acerca de cómo se encontraba y sobre sus deseos futuros, Brink encontró un camino salvador: hizo una pregunta científica. “¿Cómo fue que logró resolver entonces el problema con el...?”

Salvo el científico japonés y el miembro del jurado que formuló la pregunta, casi nadie entendió de qué problema de la física teórica se trataba.

Edymar Gonzalez A
19.502.773
CRF

http://www.jornada.unam.mx/2008/10/08/index.php?section=ciencias&article=a02n1cie

Ruptura espontánea de simetría

En física la ruptura espontánea de la simetría ocurre cuando un sistema definido por una lagrangiana simétrica respecto a un grupo de simetría cae en un estado vacío que no es simétrico. Cuando eso sucede el sistema no se comporta más de forma simétrica.

El grupo de simetría puede ser discreto como el grupo espacial de un cristal, o continuo como un grupo de Lie como la simetría rotacional del espacio. Sin embargo, si el sistema solo tiene una dimensión espacial entonces solo las simetrías discretas pueden romperse en un estado vacío de la teoría cuántica, aunque también una solución clásica puede romper una simetría continua.

La ruptura de la simetría conlleva la aparición de nuevas partículas (asociados a nuevos términos de masas en el nuevo lagrangiano como los bosones de Nambu-Goldstone o los bosones de Higgs) y la aparición de términos de masas de partículas ya existentes en el lagrangiano.

Un ejemplo común para explicar este fenómeno es el de un balón situado en reposo en la cima de una colina lo cual significa que el balón está en un estado de simetría, sin embargo, este estado es inestable ya que a la menor perturbación el balón rodaría abajo de la colina en una dirección particular alrededor de la cima.

Mecanismos que llevan a la ruptura de la simetría



Gráfica de la ruptura de simetría espontánea de la función

Mecanismo de Nambu-Goldstone

Este mecanismo se aplica al caso de una ruptura de simetría gauge global, como caso particular y sencillo de simetría gauge local. Si la L es invariante bajo una cierta simetría pero el estado del vacío no entonces se dice que el sistema tiene una "simetría en modo Goldstone" y conlleva la existencia de campos extras.

Teorema de Nambu-Goldstone

Se puede demostrar que si partículas sin masa (bosones de Nambu-Goldstone).

Ejemplo matemático

Un campo roto espontáneamente se describe mediante una teoría de campo escalar. En física, podemos ver la ruptura de simetría a través del Lagrangiano




y es en el término potencial (V(φ)) donde la acción de la ruptura de simetría ocurre. Un ejemplo de un potencial se muestra en la gráfica de la derecha.




Este potencial tiene varios estados vacíos mínimos posibles dados por



para alguna θ real entre 0 2π. El sistema también tiene un estado vacío inestable correspondiente a Φ = 0. Este estado simetría U(1). Sin embargo, en cuanto el sistema cae en un estado vacío estable específico (correspondiente a la elección de θ) esta simetría se perderá o romperá espontáneamente.

Mecanismo de Higgs

En el modelo estándard, la ruptura espontánea de simetría se complementa por el uso del bosón de Higgs que es responsable de las masas de los bosones W y Z. Todo esto puede verse de forma más técnica en la interacción de Yukawa donde se muestra como obtienen masa los fermiones mediante la ruptura de simetría. Este mecanismo se aplica al caso de una ruptura de simetría gauge local.

Concepto más amplio
Generalmente, podemos tener ruptura espontánea de simetría en situaciones donde no hay estados vacíos y para sistemas que no están descritos por una acción (integral en el tiempo del Lagrangiano). El concepto crucial aquí es el orden del parámetro. Si existe un campo que adquiere un valor de expectación (no necesariamente en el vacío) el cual no es invariante bajo la simetría en cuestión, decimos que el sistema está en una fase ordenada y la simetría se rompe espontáneamente. Esto se debe a que otros subsistemas interactúan con un parámetro de orden el cual forma un marco de referencia contra el cual se puede medir.

Si un estado vacío obedece la simetría inicial entonces se dice que el sistema está en un modo de Wigner, de otra forma se encuentra en un modo de Goldstone.

Ejemplos

• Para materiales ferromagnéticos, las leyes que los describen son invariantes bajo rotaciones espaciales. Aquí, el parámetro de orden es la magnetización, la cual mide la densidad del dipolo magnético. Arriba de la temperatura de Curie, el parámetro de orden es cero, lo cual es invariante espacialmente y no hay ruptura de simetría. Por debajo de la temperatura de Curie, sin embargo, la magnetización adquiere una constante (en la situación idealizada donde tenemos equilibrio completo; de otra forma, la simetría traslacional se rompe) con valor distinto de cero que apunta en cierta dirección. Las simetrías rotacionales residuales que dejan la orientación de este vector invariante permanecen sin romperse pero las otras rotaciones se rompen espontáneamente.

• Las leyes que describen un sólido son invariantes bajo el grupo Euclideano completo, pero el mismo sólido rompe espontáneamente este grupo degradándolo hasta el grupo espacial. El desplazamiento y la orientación son los parámetros de orden.

• Las leyes de la física son invariantes espacialmente, pero en la superficíe de la Tierra, tenemos un campo gravitacional (que en este caso juega el papel de parámetro de orden) el cual apunta hacia abajo, rompiendo la simetría rotacional completa. Esto explica por que arriba, abajo y las direcciones verticales son todas diferentes pero todas las direcciones horizontales permanecen isotrópicas.

• La relatividad general tiene una simetría de norma y de Lorentz, pero en los modelos cosmológicos FRW, la tetra velocidad media del campo definida al promediar sobre las velocidades de las galaxias (las galaxias actúan como partículas de gas a escalas cosmológicas) actúa como un parámetro de orden rompiendo esta simetría.

• En la Tierra, la invariancia Galileana (en la aproximación no relativista) se rompe por el campo de velocidad del sistema Tierra-Atmósfera, que actúa como el parámetro de orden. Esto explica por que los cuerpos móviles tienden al reposo aún antes de las explicaciones de Galileo. No tendemos a estar cuidadosos de las simetrías rotas.

• Para el modelo electrodébil, el campo de Higgs actúa como el parámetro de orden rompiendo la simetría de norma electrodébil y degradándola hacia la simetría de norma electromagnética. Al igual que en el caso ferromagnético, existe una transición de fase en la temperatura electrodébil.

• Para superconductores, hay un campo ψ de materia condensada colectiva el cual actúa como parámetro de orden rompiendo la simetría de norma electromagnética.

• En relatividad general, un difeomorfismo covariante se rompe por el parámetro de orden distinto de cero, el campo tensor métrico.

• Tomen una regla plana de plástico la cual es idéntica en ambos lados y junten los extremos. Antes de torcerla, el sistema es simétrico bajo la [reflexión (matemáticas)|[reflexión]] alrededor del plano de la regla.

• Considere una capa uniforme de fluido sobre un plano horizontal. Este sistema tiene todas las simetrías del plano Euclideano. Pero ahora caliente la parte de abajo de la superficie de forma uniforme tal que su temperatura se mayor a la de la parte de arriba.

• Cuando el gradiente de temperatura se vuelve suficientemente grande, se formarán céluas de convección, rompiendo la simetría Euclideana.

• Considere un grano en un aro circular el cual es rotado alrededor de un diámetro vertical. Como la velocidad rotacional se incrementa gradualmente desde el reposo, el grano estará en su punto inicial de equilibrio en el fondo del aro (intuitivamente estable, en su potencial gravitacional más bajo). A cierta velocidad rotacional crítica, este punto será inestable y el grano saltará hacia otro punto de equilibrio equidistante desde el centro. Inicialmente, el sistema es simétrico respecto del diámetro, aún después de pasar la velocidad crítica, el grano debe elegir entre dos nuevos puntos de equilibrio rompiendo la simetría. Esto es un análogo mecánico en dos dimensiones de la ruptura de simetría que ocurre en el campo del bosón de Higgs.

Premio Nóbel

El 7 de octubre de 2008, la Real Academia Sueca de Ciencias concedió el premio Nóbel de Física a dos Japoneses y un Americano por su trabajo en física de partículas. Makoto Kobayashi y Toshihide Maskawa compartieron con Yoichiro Nambu el premio por descubrir el origen de la ruptura de simetría y su mecanismo.


Edymar Gonzalez A
CRF
C.I: 19.502.773

http://es.wikipedia.org/wiki/Ruptura_espont%C3%A1nea_de_simetr%C3%ADa

The universal behavior of a disordered system

The Landau theory of phase transitions and the concept of symmetry breaking provide a unifying description of even such seemingly different many-body systems as a paramagnet cooled to the verge of ferromagnetic order or a metal approaching the superconducting transition. What happens, however, when these systems can lose energy to their environment? For example, in rare-earth compounds called “heavy-fermion” materials, the f-shell magnetic moments interact with a sea of mobile electrons [1]. Similarly, near the metal-superconductor transition in ultrathin wires, the electrons pair up in a connected network of small, superconducting puddles that are surrounded by a bath of unpaired metallic electrons [2]. The surrounding metal gives rise to a parallel resistive channel and hence dissipation. Introducing dissipation into a many-body quantum mechanical problem presented a theoretical challenge that was only resolved in the last quarter of the 20th century [3, 4, 5].

Phase transitions in quantum systems with both dissipation and disorder are, not surprisingly, even more complicated. Whether we like it or not, all experimental systems, and especially the examples above, have some degree of disorder such as a structural imperfection or the presence of impurities. Therefore understanding the effects of disorder is not merely an abstract intellectual challenge, it is necessary for explaining what we actually measure in these systems. In particular, even a small amount of disorder can have a big effect in low-dimensional quantum systems, where ordering is more difficult and interaction effects are enhanced. A notable example is Philip Anderson’s discovery of localization in metals (see his Nobel address [6]).

In a paper appearing in Physical Review B, Thomas Vojta and Chetan Kotabage of the Missouri University of Science and Technology and José Hoyos, now at Duke University, provide yet another example of the profound impact that disorder has on a large class of low-dimensional quantum systems [7]. In their paper, they derive the theory for a quantum phase transition in a one-dimensional system that is akin to both the magnetic and superconducting examples noted above: a chain of magnetic moments, whose motion is dissipative, and whose local interaction parameters are random. Unlike previous work, Vojta, Kotabage, and Hoyos tackle both dissipation and randomness on equal footing. Despite the complexity of this problem, they find the low-energy behavior of such dissipative random chains through a series of intuitive and simple arguments. Furthermore, they demonstrate that the low-energy behavior is independent of the type and amount of disorder in the chain. That is, it is universal.

To understand this perhaps unintuitive result, we first discuss the concept of universality and explain how it arises in random systems using a simple example. The term universality entered our vocabulary with the development of renormalization group theory, which was based on the realization that an important but overlooked symmetry of nature is scale invariance [8]. This symmetry is not omnipresent. Rather, it describes systems at critical points on the boundary between two phases, for instance, between a ferromagnet and a paramagnet. As a paramagnet is cooled to the verge of ferromagnetism, finite, strongly magnetized droplets start to form, albeit with each droplet pointing in a different direction. At the critical point, these droplets appear in all sizes, and if we zoom out, the size distribution of the droplets looks the same. But, if zooming out leaves the system looking the same, this is equivalent to saying that microscopic details are unimportant in determining the magnet’s behavior. This insensitivity to microscopic details is called universality. (We should add that in a quantum system, zooming out is tantamount to only looking at fluctuations on large length scales, or, equivalently, at the low-energy behavior.)

Typically, the description of a nondisordered, many-body quantum system begins with translational invariance and momentum conservation. Such a system of particles can be described by a set of states with a well-defined momentum denoted by the wave number k. A useful example of a simple many-body problem that we can solve in this way is the one-dimensional “tight-binding” model of noninteracting fermions, in which each fermion is tightly bound to a site on a chain, but can hop to a neighboring site with probability t. The energy spectrum for this model has a simple form: εk=-2t cos(k).

What happens, however, when translational invariance is broken? For our purposes, we can still use the hopping-fermion model, but let the hopping strength t depend on where the fermion is on the chain: t⇒ti. Instinctively, we would anticipate that the appearance of nonuniformity in this fermion-hopping system would mangle the neat cosine form of the energy spectrum and replace it with a random and noisy spectrum that crucially depends on the details of how the hopping varies from site to site. Quite surprisingly, however, the opposite seems to occur: the disorder introduced through the randomness in the hopping gives rise to an energy spectrum of the fermion states that, albeit different from the pure system’s cosine spectrum, is essentially independent of the details of the disorder. This is also the essence of universality in disordered quantum systems: the low-energy physical properties are independent of the disorder distribution.

The system that Vojta, Kotabage, and Hoyos analyze has much in common with the simple fermion-hopping problem, and it can be solved by the same method: real-space renormalization group. Shang-keng Ma, Chandan Dasgupta, and Chin-kun Hu of the University of California, San Diego proposed this method in 1979 to solve the problem of random interactions between spins on a chain [9]. We can demonstrate and use their basic arguments to understand the random-hopping problem described above.

We begin by concentrating on the strongest hopping element, tmax, and ignore everything else in the Hamiltonian as a much weaker perturbation. A fermion put in two neighboring sites, say 1 and 2, with tmax hopping between them, can minimize its energy by choosing to be in the symmetric superposition |ϕ〉=|1〉+|2〉, which has the energy ε-=-tmax. In fact, this fermion gets stuck in this bond between the two sites, since anywhere else it would have a higher energy. But fermions from neighboring sites, say site 0, can also hop to site 1, locking the first fermion inserted in the bond between the two sites at site 2. This is an excited state with energy ε=0. This predicament can resolve itself with the fermion of site 2 hopping to site 3, leaving one fermion behind in the state |ϕ〉=|1〉+|2〉 with energy of ε=-tmax. This looks as if a fermion hopped directly from site 0 to site 3, leaving the two sites 1 and 2 untouched. So, we might as well forget sites 1 and 2 and solve a new Hamiltonian in which a small “renormalized” t0,3 connects sites 0 and 3. Repeating this procedure with the strongest bond at each stage will result in all fermions inserted localized between two sites, which can be arbitrarily far apart (Fig. 1). From this procedure, we can extract the energy of the fermions’ states: a fermion localized between two sites L links apart will have a binding energy E obeying ln E~-(L)1/2 [10].

Vojta, Kotabage, and Hoyos have shown that a similar real-space analysis applies quite generally to dissipative disordered chains on the verge of a symmetry-breaking phase transition. Their focus is on a system that is similar to a chain of dynamically fluctuating magnetons (magnetic moments that can be described by a single variable). Each magneton interacts ferromagnetically with its nearest neighbors and has an energy scale ri associated with its dynamic fluctuations. These fluctuations compete with the energy scale Ji that prefers neighboring magnetons to align with one another and seeks to establish magnetic order. Just as we solved the hopping-fermion problem above, Vojta, Kotabage, and Hoyos show that we can solve the disordered dissipative quantum magnet by either (a) iteratively eliminating the most fluctuating magneton (the moment with the largest ri), which results in a ferromagnetic interaction between its neighbors, or (b) allowing the two most strongly interacting neighbors (i.e., those with the strongest Ji between them), to unite and form a single magneton, with a renormalized lower energy scale, r, of the dynamic fluctuations. A sketch of the resulting state is shown in the bottom of Fig. 2. This, they show, results in essentially the same universal behavior as is found in fermions in the random-hopping chain. Physically, this problem describes the critical behavior of superconducting puddles that form in a metallic wire right above the superconducting transition temperature (top of Fig. 2 ).

Vojta, Kotabage, and Hoyos go beyond solving the model to show that dissipative one-dimensional systems close to criticality are always susceptible to disorder. The ground-state properties of such systems cannot be analyzed using perturbation theory near the point of translational invariance. The results force us to reevaluate much of the research done on superconducting wires and magnetic chains, and to pose the question: How many other low-dimensional electronic systems can be described in the same way and have the same low-energy properties? What properties, so far taken for granted, are altered due to the presence of even a small amount of disorder? As the work of Vojta, Kotabage, and Hoyos proves, the combination of disorder, interactions, and low dimensionality (which enhances fluctuations) is bound to provide us with more surprises and fascinating examples of disorder-dominated phases, waiting to be discovered.

Illustration: Alan Stonebraker

Separate Window | Enlarge

Figure 1: Fermions on the random-hopping chain. Instead of moving freely throughout the chain, fermions are confined to pairs of sites (connected by the arcs), which are often nearest neighbors, but can also be very far apart. The pair formation is scale invariant: if we zoom out, and only draw sites that are separated by a distance matching our new reduced resolution, the localization pattern looks the same.

Illustration: Alan Stonebraker

Separate Window | Enlarge

Figure 2: (top) The model from Vojta, Kotabage, and Hoyos can describe what happens when an ultrathin metallic wire is cooled to the verge of turning into a superconductor. Superconducting puddles (orange) are connected to their neighbors through “weak links“ in a metallic environment. Because the superconductivity in each puddle is described by a complex order parameter, the puddles can be modeled as planar magnetons, with a magnitude and direction that correspond to the amplitude and phase of the order parameter, respectively. The metallic environment induces dissipation and dampens fluctuations of the order parameter. (bottom) Restricting ourselves to the language of magnetons, we sketch out how the details on small length scales become unimportant to the description of the system. Grain 4 fluctuates so much that its effective magnetic moment is destroyed. Next, grains 2 and 3 unite because of the strong magnetic coupling between them, and point in the same direction, but they too can diminish due to strong resulting fluctuations. Finally, grains 1 and 5 unite due to a resulting coupling between them.

http://physics.aps.org/articles/v2/1

Edymar Gonzalez A

C.I:19.502.773

CRF

Quantum Entanglement Achieved in Solid-State Circuitry

ScienceDaily (Jan. 12, 2010) — For the first time, physicists have convincingly demonstrated that physically separated particles in solid-state devices can be quantum-mechanically entangled. The achievement is analogous to the quantum entanglement of light, except that it involves particles in circuitry instead of photons in optical systems.

Both optical and solid-state entanglement offer potential routes to quantum computing and secure communications, but solid-state versions may ultimately be easier to incorporate into electronic devices.

In optical entanglement experiments, a pair of entangled photons may be separated via a beam splitter. Despite their physical separation, the entangled photons continue to act as a single quantum object. A team of physicists from France, Germany and Spain has now performed a solid-state entanglement experiment that uses electrons in a superconductor in place of photons in an optical system.

As conventional superconducting materials are cooled, the electrons they conduct entangle to form what are known as Cooper pairs. In the new experiment, Cooper pairs flow through a superconducting bridge until they reach a carbon nanotube that acts as the electronic equivalent of a beam splitter. Occasionally, the electrons part ways and are directed to separate quantum dots -- but remain entangled. Although the quantum dots are only a micron or so apart, the distance is large enough to demonstrate entanglement comparable to that seen in optical systems.

In addition to the possibility of using entangled electrons in solid-state devices for computing and secure communications, the breakthrough opens a whole new vista on the study of quantum mechanically entangled systems in solid materials.

The experiment is reported in an upcoming issue of Physical Review Letters and highlighted with a Viewpoint in the January 11 issue of Physics.

This is an SEM image of a typical Cooper pair splitter. The bar is 1 micrometer. A central superconducting electrode (blue) is connected to two quantum dots engineered in the same single wall carbon nanotube (in purple). Entangled electrons inside the superconductor can be coaxed to move in opposite directions in the nanotube, ending up at separate quantum dots, while remaining entangled. (Credit: L.G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk)

http://www.sciencedaily.com/releases/2010/01/100111091222.htm

Edymar Gonzalez A

C.I: 19.502.773

CRF

Why Certain Symmetries Are Never Observed in Nature

ScienceDaily (Mar. 31, 2010) — Nature likes some symmetries, but dislikes others. Ordered solids often display a so-called 6-fold rotation symmetry. To achieve this kind of symmetry, the atoms in a plane surround themselves with six neighbours in an arrangement similar to that found in honeycombs. As opposed to this, ordered materials with 7-fold, 9-fold or 11-fold symmetries are never observed in nature.

Researchers from the Max Planck Institute for Metals Research, the University of Stuttgart and the TU Berlin discovered the reason for this when they tried to impose a 7-fold symmetry on a layer of charged colloidal particles using strong laser fields: the emergence of ordered structures requires the presence of specific sites where the corresponding order nucleates. Indeed, such nuclei are present in large numbers in exactly those structures for which nature shows a preference. In contrast, they only arise sporadically in patterns with 7-fold symmetry.

The process involved here sounds unwieldy, but is, in fact, quite simple: a material has a 6-fold rotation symmetry if the arrangement of its atoms remains unchanged when it is rotated by 60 degrees -- one sixth of a circle. The atoms in metals often order themselves in this way. However, more complicated structures with 5-fold, 8-fold or 10-fold rotation symmetry also exist. "It is surprising that materials with 7-fold, 9-fold or 11-fold symmetry have not yet been observed in nature," says Clemens Bechinger, fellow at the Max Planck Institute for Metals Research and Professor at the University of Stuttgart: "This is all the more astonishing in view of the fact that patterns with any rotation symmetry can be drawn without difficulty on paper." The question is, therefore, whether such materials have simply been overlooked up to now or whether nature has an aversion to certain symmetries.

This is the question that Clemens Bechinger has been investigating with his colleagues. "The answer is of interest to us both from a fundamental point of view but also because it could be helpful for tailoring materials with novel properties for technical applications," explains the physicist. The characteristics of a material are generally very dependent on its rotation symmetry. Graphite and diamond, for example, both consist of carbon atoms and differ solely in their crystal symmetry.

To produce materials with 7-fold symmetry, which do not actually exist in nature, the researchers resorted to a special trick: they superimposed seven laser beams and thereby generated a light pattern with 7-fold symmetry. They then introduced a layer of colloidal particles approximately three micrometers in diameter into the laser field. The effect of the electromagnetic field of the light pattern on the particles is akin to the formation of a mountain landscape, in which they tend to gravitate to the valleys. The colloidal particles, which repel each other because of their electric charges, attempt, in turn, to form a 6-fold symmetrical structure.

The researchers raise the profile of the light landscape by gradually increasing the intensity of the lasers. In this way, they exert increasing pressure on the colloidal particles to form a 7-fold symmetry instead of a 6-fold one. "This enables us to ascertain the laser intensity up to which the particles do not adept the 7-fold order and retain their 6-fold symmetry," says Jules Mikhael, the doctoral student working on the project.

In the same way, the physicists subjected the particles to a 5-fold light lattice and observed a clear difference: the particles clearly avoid a 7-fold symmetry and assume the 5-fold symmetry at relatively low laser intensities. Therefore, nature's rejection of 7-fold symmetries is also demonstrated in the model system created by the researchers in Stuttgart.

"What is crucial, however, is that our experiment also uncovers the reason why the particles stubbornly refuse to form a 7-fold structure," notes Clemens Bechinger. When the physicists increase the laser intensity, the particles initially only assume a 7-fold symmetry in very isolated places. Only when the intensity is further increased does the order spread to the entire sample. The researchers identified certain structures in the light pattern as the starting point for the 7-fold symmetry. These consist of a central point of light, which is surrounded by a ring of other light points and is, therefore, strongly reminiscent of a flower blossom.

"In the light pattern with 5-fold symmetry we find around 100 times more of these flower-shaped centres than in that with the 7-fold pattern," explains Michael Schmiedeberg. The density of these nuclei clearly plays the crucial role. The higher the density, the less force the researchers must exert to generate structures of the corresponding rotation symmetry. In this case, low light intensity is sufficient for the relevant order to spread from the centre.

The differences in the densities of the flower-shaped nuclei alone also explains why 8-fold and 10-fold symmetries arise in nature but 9-fold and 11-fold ones do not. "The result is astonishing because it involves a simple geometric argument," says Bechinger: "It is completely independent on the special nature of the interaction between the particles, and applies, therefore, both to our colloidal systems and to atomic systems."

The experiments explain, first, why it is no coincidence that materials with certain symmetries are not found in nature. Second, they demonstrate a concrete way, in which such structures can be made artificially in colloidal systems -- that is with the help of external fields. This could be useful for the production of photonic crystals with unusual symmetries in which, for example, individual layers of colloids with 7-fold rotation symmetry are stacked on top of each other. Photonic crystals consist of microstructures, which affect light waves in a similar way to that in which crystal lattices affect electrons. Due to the higher rotation symmetry, the optical characteristics of 7-fold photonic crystals would be less dependent on the angle of incidence of a beam of light than the existing photonic crystals with 6-fold symmetry.

In addition to this, materials with unconventional symmetries have other interesting characteristics, for example very low frictional resistance. As a result they can reduce the friction between sliding parts e.g. in engines when applied as thin surface coatings. "Overall the search for materials with unusual rotation symmetries is of considerable interest," says Clemens Bechinger: "Our results can help to identify the particular symmetries that are worth looking for."

Symmetry bears flowers: The Stuttgart-based researchers generate light patterns by superimposing several laser beams. Flower-shaped structures form in the laser patterns which act as a nucleus for order. They arise very rarely in the 7-fold pattern (bottom left) - therefore no materials with a 7-fold symmetry are found in nature. (Credit: Jules Mikhael, University of Stuttgart)


http://www.sciencedaily.com/releases/2010/03/100330102747.htm

Edymar Gonzalez A

19.502.773

CRF

Examine the Elementary Excitations

Its amazing how slow human beings are. The atoms inside your eyelash collide with one another a million million times during each time you blink your eye. It's not surprising, then, that we spend most of our time in condensed--matter physics studying those things in materials that happen slowly. Typically only vast conspiracies of immense numbers of atoms can produce the slow behavior that humans can perceive.

Figure 8. One dimensional crystal: phonons.
The order parameter field for a one--dimensional crystal is the local displacement u(x). Long-wavelength waves in u(x) have low frequencies, and cause sound.
Crystals are rigid because of the broken translational symmetry. Because they are rigid, they fight displacements. Because there is an underlying translational symmetry, a uniform displacement costs no energy. A nearly uniform displacement, thus, will cost little energy, and thus will have a low frequency. These low-frequency elementary excitations are the sound waves in crystals.

A good example is given by sound waves. We won't talk about sound waves in air: air doesn't have any broken symmetries, so it doesn't belong in this lecture. Consider instead sound in the one-dimensional crystal shown in figure 8. We describe the material with an order parameter field u(x), where here x is the position within the material and x - u(x) is the position of the reference atom within the ideal crystal.

Now, there must be an energy cost for deforming the ideal crystal. There won't be any cost, though, for a uniform translation: u(x)u0 has the same energy as the ideal crystal. (Shoving all the atoms to the right doesn't cost any energy.) So, the energy will depend only on derivatives of the function u(x). The simplest energy that one can write looks like

(2)

(Higher derivatives won't be important for the low frequencies that humans can hear.) Now, you may remember Newton's law F=m a. The force here is given by the derivative of the energy F=-(d/du). The mass is represented by the density of the material . Working out the math (a variational derivative and an integration by parts, for those who are interested) gives us the equation

(3)

The solutions to this equation

(4)

represent phonons or sound waves. The wavelength of the sound waves is , and the frequency is . Plugging (4) into (3) gives us the relation

(5)

The frequency gets small only when the wavelength gets large. This is the vast conspiracy: only huge sloshings of many atoms can happen slowly. Why does the frequency get small? Well, there is no cost to a uniform translation, which is what (4) looks like for infinite wavelength. Why is there no energy cost for a uniform displacement? Well, there is a translational symmetry: moving all the atoms the same amount doesn't change their interactions. But haven't we broken that symmetry? That is precisely the point.

Long after phonons were understood, Jeffrey Goldstone started to think about broken symmetries and order parameters in the abstract. He found a rather general argument that, whenever a continuous symmetry (rotations, translations, SU(3), ...) is broken, long-wavelength modulations in the symmetry direction should have low frequencies. The fact that the lowest energy state has a broken symmetry means that the system is stiff: modulating the order parameter will cost an energy rather like that in equation equation (2). In crystals, the broken translational order introduces a rigidity to shear deformations, and low frequency phonons (figure 8). In magnets, the broken rotational symmetry leads to a magnetic stiffness and spin waves (figure 9a). In nematic liquid crystals, the broken rotational symmetry introduces an orientational elastic stiffness (it pours, but resists bending!) and rotational waves (figure 9b).

Figure 9A. Magnets: spin waves.
Magnets break the rotational invariance of space. Because they resist twisting the magnetization locally, but don't resist a uniform twist, they have low energy spin wave excitations.

Figure 9B. Nematic liquid crystals: rotational waves.
Nematic liquid crystals also have low-frequency rotational waves.

In superfluids, the broken gauge symmetry leads to a stiffness which results in the superfluidity. Superfluidity and superconductivity really aren't any more amazing than the rigidity of solids. Isn't it amazing that chairs are rigid? Push on a few atoms on one side, and atoms away atoms will move in lock-step. In the same way, decreasing the flow in a superfluid must involve a cooperative change in a macroscopic number of atoms, and thus never happens spontaneously any more than two parts of the chair ever drift apart.

The low-frequency Goldstone modes in superfluids are heat waves! (Don't be jealous: liquid helium has rather cold heat waves.) This is often called second sound, but is really a periodic modulation of the temperature which passes through the material like sound does through a metal.

O.K., now we're getting the idea. Just to round things out, what about superconductors? They've got a broken gauge symmetry, and have a stiffness to decays in the superconducting current. What is the low energy excitation? It doesn't have one. But what about Goldstone's theorem? Well, you know about physicists and theorems ...

That's actually quite unfair: Goldstone surely had conditions on his theorem which excluded superconductors. It's just that everybody forgot the extra conditions, and just remembered that you always got a low frequency mode when you broke a continuous symmetry. We of course understood all along why there isn't a Goldstone mode for superconductors: my advisor, Phillip W. Anderson, showed that it's related to the Meissner effect. The high energy physicists forgot, though, and had to rediscover it for themselves. Now we all call the loophole in Goldstone's theorem the Higgs mechanism, because (to be truthful) Higgs and his high-energy friends found a much simpler and more elegant explanation than we had. We'll discuss Meissner effects and the Higgs mechanism in the next lecture.

I'd like to end this section, though, by bringing up another exception to Goldstone's theorem: one we've known about even longer, but which we don't have a nice explanation for. What about the orientational order in crystals? Crystals break both the continuous translational order and the continuous orientational order. The phonons are the Goldstone modes for the translations, but there are no orientational Goldstone modes. We'll discuss this further in the next lecture, but I think this is one of the most interesting unsolved basic questions in the subject.

Examine the Elementary Excitations

ts amazing how slow human beings are. The atoms inside your eyelash collide with one another a million million times during each time you blink your eye. It's not surprising, then, that we spend most of our time in condensed--matter physics studying those things in materials that happen slowly. Typically only vast conspiracies of immense numbers of atoms can produce the slow behavior that humans can perceive.

Figure 8. One dimensional crystal: phonons.
The order parameter field for a one--dimensional crystal is the local displacement u(x). Long-wavelength waves in u(x) have low frequencies, and cause sound.
Crystals are rigid because of the broken translational symmetry. Because they are rigid, they fight displacements. Because there is an underlying translational symmetry, a uniform displacement costs no energy. A nearly uniform displacement, thus, will cost little energy, and thus will have a low frequency. These low-frequency elementary excitations are the sound waves in crystals.

A good example is given by sound waves. We won't talk about sound waves in air: air doesn't have any broken symmetries, so it doesn't belong in this lecture. Consider instead sound in the one-dimensional crystal shown in figure 8. We describe the material with an order parameter field u(x), where here x is the position within the material and x - u(x) is the position of the reference atom within the ideal crystal.

Now, there must be an energy cost for deforming the ideal crystal. There won't be any cost, though, for a uniform translation: u(x)u0 has the same energy as the ideal crystal. (Shoving all the atoms to the right doesn't cost any energy.) So, the energy will depend only on derivatives of the function u(x). The simplest energy that one can write looks like

(2)

(Higher derivatives won't be important for the low frequencies that humans can hear.) Now, you may remember Newton's law F=m a. The force here is given by the derivative of the energy F=-(d/du). The mass is represented by the density of the material . Working out the math (a variational derivative and an integration by parts, for those who are interested) gives us the equation

(3)

The solutions to this equation

(4)

represent phonons or sound waves. The wavelength of the sound waves is , and the frequency is . Plugging (4) into (3) gives us the relation

(5)

The frequency gets small only when the wavelength gets large. This is the vast conspiracy: only huge sloshings of many atoms can happen slowly. Why does the frequency get small? Well, there is no cost to a uniform translation, which is what (4) looks like for infinite wavelength. Why is there no energy cost for a uniform displacement? Well, there is a translational symmetry: moving all the atoms the same amount doesn't change their interactions. But haven't we broken that symmetry? That is precisely the point.

Long after phonons were understood, Jeffrey Goldstone started to think about broken symmetries and order parameters in the abstract. He found a rather general argument that, whenever a continuous symmetry (rotations, translations, SU(3), ...) is broken, long-wavelength modulations in the symmetry direction should have low frequencies. The fact that the lowest energy state has a broken symmetry means that the system is stiff: modulating the order parameter will cost an energy rather like that in equation equation (2). In crystals, the broken translational order introduces a rigidity to shear deformations, and low frequency phonons (figure 8). In magnets, the broken rotational symmetry leads to a magnetic stiffness and spin waves (figure 9a). In nematic liquid crystals, the broken rotational symmetry introduces an orientational elastic stiffness (it pours, but resists bending!) and rotational waves (figure 9b).

Figure 9A. Magnets: spin waves.
Magnets break the rotational invariance of space. Because they resist twisting the magnetization locally, but don't resist a uniform twist, they have low energy spin wave excitations.

Figure 9B. Nematic liquid crystals: rotational waves.
Nematic liquid crystals also have low-frequency rotational waves.

In superfluids, the broken gauge symmetry leads to a stiffness which results in the superfluidity. Superfluidity and superconductivity really aren't any more amazing than the rigidity of solids. Isn't it amazing that chairs are rigid? Push on a few atoms on one side, and atoms away atoms will move in lock-step. In the same way, decreasing the flow in a superfluid must involve a cooperative change in a macroscopic number of atoms, and thus never happens spontaneously any more than two parts of the chair ever drift apart.

The low-frequency Goldstone modes in superfluids are heat waves! (Don't be jealous: liquid helium has rather cold heat waves.) This is often called second sound, but is really a periodic modulation of the temperature which passes through the material like sound does through a metal.

O.K., now we're getting the idea. Just to round things out, what about superconductors? They've got a broken gauge symmetry, and have a stiffness to decays in the superconducting current. What is the low energy excitation? It doesn't have one. But what about Goldstone's theorem? Well, you know about physicists and theorems ...

That's actually quite unfair: Goldstone surely had conditions on his theorem which excluded superconductors. It's just that everybody forgot the extra conditions, and just remembered that you always got a low frequency mode when you broke a continuous symmetry. We of course understood all along why there isn't a Goldstone mode for superconductors: my advisor, Phillip W. Anderson, showed that it's related to the Meissner effect. The high energy physicists forgot, though, and had to rediscover it for themselves. Now we all call the loophole in Goldstone's theorem the Higgs mechanism, because (to be truthful) Higgs and his high-energy friends found a much simpler and more elegant explanation than we had. We'll discuss Meissner effects and the Higgs mechanism in the next lecture.

I'd like to end this section, though, by bringing up another exception to Goldstone's theorem: one we've known about even longer, but which we don't have a nice explanation for. What about the orientational order in crystals? Crystals break both the continuous translational order and the continuous orientational order. The phonons are the Goldstone modes for the translations, but there are no orientational Goldstone modes. We'll discuss this further in the next lecture, but I think this is one of the most interesting unsolved basic questions in the subject.

http://www.lassp.cornell.edu/sethna/OrderParameters/ElementaryExcitations.html

Edymar Gonzalez A

19.502.773

CRF