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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Ensamble de Gibbs generalizado a partir del Hamiltoniano de entrelazamiento de estados propios

Hao Chen1,2, Biao Lian1

  • 1Princeton University, Department of Physics, Princeton, New Jersey 08544, USA.

Physical review letters
|December 19, 2025
PubMed
Resumen

Los investigadores proponen un nuevo marco que utiliza hamiltonianos de entrelazamiento para encontrar cantidades conservadas para ensambles de Gibbs generalizados (GGE). Este GGE no abeliano predice de manera más precisa la relajación en sistemas cuánticos como fermiones libres y bosones duros.

Palabras clave:
ensambles de Gibbs generalizadosHamiltoniano de entrelazamientocantidades conservadassistemas cuánticosdinámica de relajaciónfermiones libresbosones durosfísica estadística cuánticaintegrabilidad cuántica

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Área de la Ciencia:

  • Mecánica cuántica
  • Mecánica estadística
  • Física de la materia condensada

Sus antecedentes:

  • Los sistemas cuánticos relajados con leyes de conservación a menudo se aproximan mediante ensambles de Gibbs generalizados (GGE).
  • GGE incorpora cantidades conservadas que actúan como integrales de movimiento.
  • El origen y el conjunto natural de estas cantidades conservadas siguen siendo un área activa de investigación.

Objetivo del estudio:

  • Proponer un marco novedoso, la supermatriz de densidad del Hamiltoniano de entrelazamiento (EHSM), para derivar cantidades conservadas en GGE.
  • Demostrar la eficacia del marco para modelos de fermiones libres.
  • Investigar las propiedades y el poder predictivo de las cantidades conservadas derivadas.

Principales métodos:

  • Establecer una analogía entre las matrices de densidad reducidas de estados propios y GGE.
  • Utilizar el marco de la supermatriz de densidad del Hamiltoniano de entrelazamiento (EHSM).
  • Identificar las cantidades conservadas como superposiciones lineales de los hamiltonianos de entrelazamiento de estados propios.

Principales resultados:

  • Un conjunto natural de cantidades conservadas para GGE surge de las matrices de densidad reducidas dentro del marco EHSM.
  • Demostración explícita para modelos mapeables a fermiones libres.
  • Las cantidades conservadas derivadas conducen a un GGE no abeliano para fermiones libres 1D y bosones duros.
  • El GGE no abeliano muestra una precisión mejorada al predecir la relajación de bilineales de fermiones y bosones en comparación con el GGE abeliano convencional.

Conclusiones:

  • El marco EHSM proporciona un método para identificar cantidades conservadas relevantes para GGE.
  • El GGE no abeliano ofrece una descripción más precisa de la dinámica de relajación en ciertos sistemas cuánticos.
  • La generalización de este marco puede ofrecer nuevos enfoques numéricos para estudiar la integrabilidad cuántica.