Properties of quantum Markovian master equations

In this paper we give an essentially self-contained account of some general structural properties of the dynamics of quantum open Markovian systems. We review some recent results regarding the problem of the classification of quantum Markovian master equations and the limiting conditions under which the dynamical evolution of a quantum open system obeys an exact semigroup law (weak coupling limit and singular coupling limit). We discuss a general form of quantum detailed balance and its relation to thermal relaxation and to microreversibility.     

On the mixing-enhancing dynamical maps and mixing-enhancing evolution of a quantum system

The mixing-enhancing (in the sense of Uhlmann) dynamical maps and dynamical evolution is studied. We give a necessary and sufficient condition for a dynamical map (and dynamical evolution) of a quantum system to be mixing-enhancing. In the case of a finite- dimensional Hilbert space this condition is equivalent to the condition that the dynamical map (dynamical evolution) preserve the most mixed state and the von Neumann entropy be non- decreasing. It is proved that, in contrast with the finite-dimensional case, increasing of the von Neumann entropy under a dynamical map (for any initial state) does not imply that the dynamical map is mixing-enhancing. We also give a necessary and sufficient condition for an infinitesimal generator of a norm-continuous dynamical semigroup to be mixing-enhancing.     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Correlation dynamics of qubit-qutrit systems in a classical dephasing environment

We study the time evolution of classical and quantum correlations for hybrid qubit-qutrit systems in independent and common dephasing environments. Our discussion involves a comparative analysis of the Markovian dynamics of negativity, quantum discord, geometric measure of quantum discord and classical correlation. For the case of independent environments, we have demonstrated the phenomenon of sudden transition between classical and quantum decoherence for qubit-qutrit states. In the common environment case, we have shown that dynamics of quantum and geometric discords might be completely independent of each other for a certain time interval, although they tend to be eventually in accord.     

Quantum Evolution beyond the Markovian Semigroup — Generalizing the Stenholm–Barnett Approach

We provide conditions for the memory kernel governing the time-nonlocal quantum master equation which guarantee that the corresponding dynamical map is completely positive and trace-preserving. This approach gives rise to the new parametrization of dynamical maps in terms of two completely positive maps – so-called legitimate pair. In fact, these new parameterizations are a natural generalization of Markovian semigroup. Interestingly our class contains recently studied models like semi-Markov evolution and collision models.     

Completely positive dynamical semigroups and quantum resonance theory

Starting from a microscopic system–environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the following two properties: It is (linearly) small in the system–environment coupling constant for all times, and it vanishes exponentially quickly in the large time limit. Our approach is based on the quantum dynamical resonance theory.     

Higher Order Quantum Onsager Coefficients from Dynamical Invariants

Functionals representing dynamical invariants under unitary quantum dynamics of open systems are used to derive Onsager coefficients for entropy production in irreversible processes if the nonunitary time evolution is determined by quantum dynamical semigroups. The procedure allows a derivation from first principles of the quantum analogue to the classical case.     

笛卡儿坐标下空间转子体系的双波函数描述

本文给出了笛卡儿坐标下空间转子体系的双波函数描述,得到了该坐标下每一个力学量的时间演化方程。因而我们的描述是完备的。经典力学运动方程是我们所得演化方程的经典极限。而通常的量子力学描述是我们描述的统计结果。本文还表明,笛卡儿坐标比球坐标能提供更多的物理内容。 关键词：     

Some remarks on dynamical semigroups

We deal with time evolution of a finite quantum system given by a dynamical semigroup Λ_t. For the semigroup we define and give some properties of the convex Λ_t-invariant subset of states “pathological” in some aspect evolving in strictly reversible manner independently of the stochastic surroundings of the system.     

Entropy increase for a class of dynamical maps

The dynamical evolution of a quantum system is described by a one parameter family of linear transformations of the space of self-adjoint trace class operators (on the Hilbert space of the system) into itself, which map statistical operators to statistical operators. We call such transformations dynamical maps. We give a sufficient condition for a dynamical map A not to decrease the entropy of a statistical operator. In the special case of an N-level system, this condition is also necessary and it is equivalent to the property that A preserves the central state.     

Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over???∞?<?t?<?+∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀?≤?t?<?+∞, for which the mathematicians would choose t ₀?=?0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time $ t_0^{(i) } $ for an ensemble of individual quanta.     

Interacting Quantum and Classical Continuous Systems II. Asymptotic Behavior of the Quantum Subsystem

In the framework of event-enhanced quantum theory the dynamical equation for the reduced density matrix of a quantum system interacting with a continuous classical system is derived. The asymptotic behavior of the corresponding dynamical semigroup is discussed. The example of a quantum–classical coupling on Lobatchevski space is presented.     

Dispersive Quantum Systems

A dispersive quantum system is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the class of completely positive Markovian quantum systems in finite dimension (through a homogeneous linear equation for the non-Hamiltonian part of the system’s Liouvillian). To set the framework, the basic features of quantum mechanics are reviewed focusing on time evolution and also on the theory of completely positive Markovian quantum systems, including Kossakowski–Lindblad’s standard form for Liouvillians. After those general considerations, a simple two-dimensional example is presented and then applied to describe the neutrino oscillation, with the introduction of a new “dispersive parameter.”