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Initial-state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states

机译:可积量子系统中猝灭动力学的初始状态依赖性。三,混沌状态

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摘要

We study sudden quantum quenches in which the initial states are selected to be either eigenstates of annintegrable Hamiltonian that is nonmappable to a noninteracting one or a nonintegrable Hamiltonian, while thenHamiltonian after the quench is always integrable and mappable to a noninteracting one. By studying weightednenergy densities and entropies, we show that quenches starting from nonintegrable (chaotic) eigenstates leadnto an “ergodic” sampling of the eigenstates of the final Hamiltonian, while those starting from the integrableneigenstates do not (or at least it is not apparent for the system sizes accessible to us). This goes in parallel withnthe fact that the distribution of conserved quantities in the initial states is thermal in the nonintegrable cases andnnonthermal in the integrable ones, and means that, in general, thermalization occurs in integrable systems whennthe quench starts form an eigenstate of a nonintegrable Hamiltonian (away from the edges of the spectrum),nwhile it fails (or requires larger system sizes than those studied here to become apparent) for quenches starting atnintegrable points.We test those conclusions by studying the momentum distribution function of hard-core bosonsnafter a quench.
机译:我们研究了突然的量子猝灭,其中初始状态被选择为不可与非相互作用的哈密顿不可映射的不可整合哈密顿量的本征态或不可整合的哈密顿量,而淬灭后的哈密尔顿则始终可与非相互作用的哈密顿量映射。通过研究加权能密度和熵,我们表明,从不可积分(混沌)本征态开始的淬灭导致最终哈密顿量本征态的“遍历”采样,而从可积分本征态开始的猝灭则没有(或至少对于该积分态不明显)。我们可以访问的系统大小)。这与以下事实并行:在不可积情况下,初始状态中守恒量的分布是热的;在可积情况下,守恒量的分布是非热的,这意味着,通常,当淬灭开始时,在不可积哈密顿量的本征态下,可热化发生在可积系统中。 (远离光谱的边缘),而在不可积分点开始的淬灭却失效了(或需要比此处研究的系统尺寸大的系统才能变得明显)。我们通过研究淬灭后硬核玻色子的动量分布函数来检验这些结论。 。

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  • 来源
    《PHYSICAL REVIEW A》 |2013年第4期|1-9|共9页
  • 作者

    Kai He; Marcos Rigol;

  • 作者单位

    Department of Physics The Pennsylvania State University University Park Pennsylvania 16802 USADepartment of Physics Georgetown University Washington DC 20057 USA;

    Department of Physics The Pennsylvania State University University Park Pennsylvania 16802 USA;

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