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arXiv:2206.00326 · Entropy

Quantum Energy Current Induced Coherence in a Spin Chain under Non-Markovian Environments

Arapat Ablimit, Run-Hong He, Yang-Yang Xie, Lian-Ao Wu, Zhao-Ming Wang

Published Oct 1, 2022• 6 citations

Abstract

We investigate the time-dependent behaviour of the energy current between a quantum spin chain and its surrounding non-Markovian and finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are assumed to be initially in thermal equilibrium at temperature Ts and Tb, respectively. This model plays a fundamental role in study of quantum system evolution towards thermal equilibrium in an open system. The non-Markovian quantum state diffusion (NMQSD) equation approach is used to calculate the dynamics of the spin chain. The effects of non-Markovianity, temperature difference and system-bath interaction strength on the energy current and the corresponding coherence in cold and warm baths are analyzed, respectively. We show that the strong non-Markovianity, weak system-bath interaction and low temperature difference will help to maintain the system coherence and correspond to a weaker energy current. Interestingly, the warm baths destroy the coherence while the cold baths help to build coherence. Furthermore, the effects of the Dzyaloshinskii-Moriya (DM) interaction and the external magnetic field on the energy current and coherence are analyzed. Both energy current and coherence will change due to the increase of the system energy induced by the DM interaction and magnetic field. Significantly, the minimal coherence corresponds to the critical magnetic field which causes the first order phase transition.

DOI: 10.3390/e24101406

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We study how the non-Markovian dynamics of an open quantum system is affected by the properties and parameters of its environment using a solvable model consisting of a single spin coupled to an Ising chain of spins with a transverse field playing the role of the environment. By solving the model's evolution exactly, we are able to calculate the memory kernel for the Nakajima-Zwanzig master equation and examine how its characteristics change with the temperature, field strength, and size of the environment. We discover that the thermal fluctuation enhances system-environment correlation in our model, leading to increased memory effect that is more prominent in larger environment and becomes dominant at higher temperatures to give rise to non-Markovian dynamics. Near the critical point of the environment, we find Fisher zeros in the Loschmidt echo exist for finite-environment sizes satisfying certain conditions, which results in exotic memory effects that can have a major impact on the system dynamics.

We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the

l_1

-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.