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Universal fluctuations around typicality for quantum ergodic systems.
Bauer, Michel; Bernard, Denis; Jin, Tony.
Afiliação
  • Bauer M; Institut de Physique Théorique de Saclay, CEA-Saclay and CNRS, 91191 Gif-sur-Yvette, France.
  • Bernard D; Département de Mathématiques et Applications, ENS-Paris, 75005 Paris, France.
  • Jin T; Laboratoire de Physique de l'Ecole Normale Supérieure de Paris, CNRS, ENS and Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France.
Phys Rev E ; 101(1-1): 012115, 2020 Jan.
Article em En | MEDLINE | ID: mdl-32069547
For a quantum system in a macroscopically large volume V, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system v≪V is almost surely totally mixed. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermalization hypothesis is discussed.

Texto completo: 1 Base de dados: MEDLINE Idioma: En Ano de publicação: 2020 Tipo de documento: Article

Texto completo: 1 Base de dados: MEDLINE Idioma: En Ano de publicação: 2020 Tipo de documento: Article