Himanshu Badhani, Subhashish Banerjee and C M Chandrashekar
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引用次数: 0
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.
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.