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.     

Measure of irreversibility and entropy production in open quantum systems

A new concept of a measure of irreversibility for quantum dynamics in open systems is introduced as a suitably regularized substitute for the common notion of entropy production, which, unfortunately, yields infinite values for so many irreversible processes of physical relevance.     

Virtues and Limitations of Markovian Master Equations with a Time-Dependent Generator

A Markovian master equation with time-dependent generator is constructed that respects basic constraints of quantum mechanics, in particular the von Neumann conditions. For the case of a two-level system, Bloch equations with time-dependent parameters are obtained. Necessary conditions on the latter are formulated. By employing a time-local counterpart of the Nakajima–Zwanzig equation, we establish a relation with unitary dynamics. We also discuss the relation with the weak-coupling limit. On the basis of a uniqueness theorem, a standard form for the generator of time-local master equations is proposed. The Jaynes–Cummings model with atomic damping is solved. The solution explicitly demonstrates that reduced dynamics can be described by time-local master equations only on a finite time interval. This limitation is caused by divergencies in the generator. A limit of maximum entropy is presented that corroborates the foregoing statements. A second limiting case demonstrates that divergencies may even occur for small perturbations of the weak-coupling regime.     

Spinpolarized OPW-band structure of magnetic semiconductors with application to EuO. Part I

The OPW-method has been generalized for the calculation of spinpolarized energy bands in magnetic semiconductors and applied to the ferromagnetic semiconductor EuO. Part I of this paper contains the general formulation of the method, a grouptheoretical analysis and qualitative predictions for the band structure. It is shown why the application of the OPW-method to heavy substances, as for instance to magnetic semiconductors, gives rise to difficulties due to instabilities in the related eigenvalue problem.     

Molecular Quantum Beat Spectroscopy in External Fields as a Sensitive Probe of Excited State Properties

The new phenomenon of the external field dependence of quantum beats in polyatomic molecules is studied on a model which offers analytical formulas for a series expansion to lowest order in the field. A comparison with recent experiments on the magnetic field effect in biacetyl suggests that, in addition to the level shift the triplet deactivation is also strongly field-dependent. New experiments are proposed.     

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.     

Spinpolarized OPW-band structure of magnetic semiconductors with application to EuO. Part II

The OPW-method has been generalized for the calculation of spinpolarized energy bands in magnetic semiconductors and applied to the ferromagnetic semiconductor EuO. Part II describes the numerical methods used in the application to EuO together with a careful consideration of numerical problems involved. Finally the results of the calculations are presented. With the aid of selection rules and Van Hove-singularities a list of allowed optical transitions has been deduced. These results compare favorably with recent experiments.     

Quantum theory of dissipative processes: The Markov approximation revisited

Adopting the standard mathematical framework for describing reduced dynamics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima-Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which govern the evolution of the density operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going beyond the Markov approximation in a controlled way. On the basis of the Bloch equations we argue once more that in studying quantum dissipation one has to pay attention to the von Neumann conditions. In the Nakajima-Zwanzig equation we make the first Born approximation. The ensuing master equation possesses the correct weak-coupling limit. While proving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling limit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation functions, we propose a physical limit in which the solutions for the density operator become Markovian in character. We confirm the well-known statement that, as seen from a macroscopic standpoint, the system starts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters and by more than 50%.