Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas
Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas
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DOI：
10.21468/scipostphys.12.1.035
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发表时间：
2021-04
期刊：
影响因子：
5.5
通讯作者：
D. Yampolsky;N. Harshman;V. Dunjko;Zaijong Hwang;M. Olshanii
中科院分区：
文献类型：
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作者：
D. Yampolsky;N. Harshman;V. Dunjko;Zaijong Hwang;M. Olshanii
我们考虑量子多体短程相互作用系统中出现混沌的玩具模型：盒子中的两个一维硬核粒子，具有小质量缺陷作为对可积系统的扰动，后者由两个等质量粒子表示。对于该系统，我们应用量子广义的奇里科夫的标准的混沌的发病，即重叠共振的标准。在那里，经典的非线性共振几乎自动转换为量子语言。量子力学在稍后阶段介入：占据少于一个哈密顿本征态的共振被排除在混沌判据之外。共振表现为低纯度的未扰动本征态的连续补丁，由未破坏的状态组分隔-经典KAM环面的量子类似物。
We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles. To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e. the criterion of overlapping resonances. There, classical nonlinear resonances translate almost automatically to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion. Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed states-the quantum analogues of the classical KAM tori.