Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction

IF 2.6 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Physica Scripta Pub Date : 2024-09-09 DOI:10.1088/1402-4896/ad753f
Himanshu Badhani, Subhashish Banerjee and C M Chandrashekar
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Abstract

A -symmetric, non-Hermitian Hamiltonian in the -unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner product map on the underlying vector space, facilitated by a ‘metric operator’. A more traditional method, however, involves treating the evolution as open system dynamics, and the state is constructed through normalization at each time step. In this work, we present a comparative study of the two methods of constructing the reduced dynamics of a system evolving under a -symmetric Hamiltonian. Our system is a one-dimensional quantum walk with the spin and position degrees of freedom forming its two subsystems. We compare the information flow between the subsystems under the two methods. We find that under the metric formalism, a power law decay of the information backflow to the subsystem gives a clear indication of the transition from -unbroken to the broken phase. This is unlike the information backflow under the normalized state method. We also note that even though non-Hermiticity models open system dynamics, pseudo-Hermiticity can increase entanglement between the subsystem in the metric Hilbert space, thus indicating that pseudo-Hermiticity cases can be seen as a resource in quantum mechanics.
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非ermitian量子行走与非马尔可夫性:硬币位置的相互作用
在 "未破碎状态 "下的非对称、非赫米特哈密顿可以在希尔伯特空间的适当选择下产生单元动力学。希尔伯特空间由底层矢量空间上与哈密顿相容的内积映射决定,并由 "度量算子 "提供便利。然而,更传统的方法是将演化视为开放系统动力学,在每个时间步通过归一化构建状态。在这项工作中,我们对这两种构建在-对称哈密顿下演化的系统还原动力学的方法进行了比较研究。我们的系统是一个一维量子行走系统,自旋和位置自由度构成了它的两个子系统。我们比较了两种方法下子系统之间的信息流。我们发现,在度量形式主义下,流向子系统的信息回流的幂律衰减清楚地表明了从 "未破碎 "阶段到 "破碎 "阶段的过渡。这与归一化状态方法下的信息回流不同。我们还注意到,即使非恒常性是开放系统动力学模型,伪恒常性也能增加公制希尔伯特空间中子系统之间的纠缠,从而表明伪恒常性情况可被视为量子力学中的一种资源。
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来源期刊
Physica Scripta
Physica Scripta 物理-物理:综合
CiteScore
3.70
自引率
3.40%
发文量
782
审稿时长
4.5 months
期刊介绍: Physica Scripta is an international journal for original research in any branch of experimental and theoretical physics. Articles will be considered in any of the following topics, and interdisciplinary topics involving physics are also welcomed: -Atomic, molecular and optical physics- Plasma physics- Condensed matter physics- Mathematical physics- Astrophysics- High energy physics- Nuclear physics- Nonlinear physics. The journal aims to increase the visibility and accessibility of research to the wider physical sciences community. Articles on topics of broad interest are encouraged and submissions in more specialist fields should endeavour to include reference to the wider context of their research in the introduction.
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