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弱可积性破缺:相干扩散中具有可积性特征的混沌

Weak Integrability Breaking: Chaos with Integrability Signature in Coherent Diffusion.

作者信息

Žnidarič Marko

机构信息

Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia.

出版信息

Phys Rev Lett. 2020 Oct 30;125(18):180605. doi: 10.1103/PhysRevLett.125.180605.

Abstract

We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of the inverse density, instead of to the inverse density as would follow from Matthiessen's rule. We show that Matthiessen's rule has to be modified in nonballistic systems. Results also highlight a nontrivial role of interacting scattering on a single impurity, and that there is a regime where adding more impurities can actually increase transport.

摘要

我们研究微扰如何影响可积多体量子系统的动力学,从而导致从可积性到混沌的转变。通过研究含杂质的海森堡链中的自旋输运,我们发现在热力学极限下,即使是无穷小的微扰也会使输运变为扩散型。因此,小的广延微扰会立即导致从可积性到混沌的转变。然而,扩散常数对杂质密度的依赖性中编码了可积性的残余,即,在小密度时,它与密度倒数的平方根成正比,而不是像 Matthiessen 规则所预测的那样与密度倒数成正比。我们表明,在非弹道系统中 Matthiessen 规则必须修正。结果还突出了单个杂质上相互作用散射的重要作用,并且存在一种情况,即添加更多杂质实际上可以增加输运。

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