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Non-Hermitian skin effect of Liouvillian superoperators in quantum open systems can induce phenomena of non-trivial damping, known as chiral/helical damping. While non-Hermitian skin effect and chiral/helical damping occur only under open boundary condition, we propose an effect called information restrain which does not rely on boundary conditions. We demonstrate that information restrain is stable against disorder and is an intrinsic property of a type of open quantum systems or non-Hermitian system. Then we define the strength of information restrain $I_R$, which describes the ratio of different decay rates of signals strengthes along opposite propagation directions. Based on information restrain, We can provide a simple and elegant explanation of chiral and helical damping, and get the local maximum of relative particle number for periodical boundary system, consistent with numerical calculations. In terms of information restrain, we also illustrate the existence of correspondence between edge modes and damping modes and deduce that there are many chiral/helical transport properties in this information restrain class.
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We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell-Bloch equation. In a resonantly driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that the Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by nonlinear processes and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of heating is a key condition for the realization of Floquet states in both on and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.
We consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, $S(T) rightarrow 0$ as $Trightarrow 0$, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that $S(T)rightarrow gln 2$ as $Trightarrow 0$, where $g$ is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy $S({bf x}; T) rightarrow 0$ as $T({bf x})rightarrow 0$, except for cases of measure zero arising due to localized states, where $T({bf x})$ is the temperature measured by a local thermometer.
Basing on the theory of Feynmans influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Kramers theorem ensures double degeneracy in the energy spectrum of a time-reversal symmetric fermionic system with half-integer total spin. Here we are now trying to go beyond the closed system and discuss Kramers degeneracy in open systems out of equilibrium. In this letter, we prove that the Kramers degeneracy in interacting fermionic systems is equivalent to the degeneracy in the spectra of different spins together with the vanishing of the inter-spin spectrum. We find the violation of Kramers degeneracy in time-reversal symmetric open quantum systems is locked with whether the system reaches thermal equilibrium. After a sudden coupling to an environment in a time-reversal symmetry preserving way, the Kramers doublet experiences an energy splitting at a short time and then a recovery process. We verified the violation and revival of Kramers degeneracy in a concrete model of interacting fermions and we find Kramers degeneracy is restored after the local thermalization time. By contrast, for time-reversal symmetry $tilde{cal T}$ with $tilde{cal T}^2=1$, we find although there is a violation and revival of spectral degeneracy for different spins, the inter-spin spectral function is always nonzero. We also prove that the degeneracy in spectral function protected by unitary symmetry can be maintained always.
Measuring local temperatures of open systems out of equilibrium is emerging as a novel approach to study the local thermodynamic properties of nanosystems. An operational protocol has been proposed to determine the local temperature by coupling a probe to the system and then minimizing the perturbation to a certain local observable of the probed system. In this paper, we first show that such a local temperature is unique for a single quantum impurity and the given local observable. We then extend this protocol to open systems consisting of multiple quantum impurities by proposing a local minimal perturbation condition (LMPC). The influence of quantum resonances on the local temperature is elucidated by both analytic and numerical results. In particular, we demonstrate that quantum resonances may give rise to strong oscillations of the local temperature along a multiimpurity chain under a thermal bias.
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