Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics
详细信息 查看全文
- 作者：Emil A. Yuzbashyan eyuzbash@physics.rutgers.edu" class="auth_mail" title="E-mail the corresponding author
- 关键词：Coherent many-body dynamics ; Quantum quenches ; Statistical ensembles ; Integrable systems ; Generalized Gibbs Ensemble ; Prethermalization
- 刊名：Annals of Physics
- 出版年：2016
- 出版时间：April 2016
- 年：2016
- 卷：367
- 期：Complete
- 页码：288-296
- 全文大小：377 K
文摘
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it to the limit of infinite number of degrees of freedom. In quantum mechanics, we prove GGE for maximal Hamiltonians—a class of models stemming from a rigorous notion of quantum integrability understood as the existence of conserved charges with prescribed dependence on a system parameter, e.g. Hubbard class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0003491616000403&_mathId=si1.gif&_user=111111111&_pii=S0003491616000403&_rdoc=1&_issn=00034916&md5=1662a54e3cca053dda3273592f3a004b" title="Click to view the MathML source">Uclass="mathContainer hidden">class="mathCode">, anisotropy in the XXZ model etc. In analogy with classical integrability, the defining property of these models is that they have the maximum number of independent integrals. We contrast their dynamics induced by quenching the parameter to that of random matrix Hamiltonians.