The Emergence of Classicality via Decoherence Described by Lindblad Operators

It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic subsystems of environments even in the absence of dynamical decoherence. It is suggested that decoherence is best regarded as explaining the persistence of true classicality, rather than the emergence, rather than the emergence of quasiclassicalit...

Decoherence of quantum systems from entanglement with an unmonitored environment is to date the most compelling explanation of the emergence of a classical picture from a quantum world. While it is well understood for a single Lindblad operator, the role in the einselection process of a complex system-environment interaction remains to be clarified. In this paper, we analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators modeli...

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry and quantum information. In close analogy to a classical Markov process, the interaction of an open quantum system with a noisy environment is often mod...

This is an introduction to the theory of decoherence with an emphasis on its microscopic origins and on a dynamic description. The text corresponds to a chapter soon to be published in: A. Buchleitner, C. Viviescas, and M. Tiersch (Eds.), Entanglement and Decoherence. Foundations and Modern Trends, Lecture Notes in Physics, Vol 768, Springer, Berlin (2009)

The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modelling the decoherence of a subsystem by its environment. Denoting the decoherence time $\tau$, we demonstrate that a double scaling limit in which $\hbar \rightarrow 0$ an...

These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relati...

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical mechanics which provides a continuous transition to quantum mechanics via environment-induced decoherence.

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.

In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which thermal fluc...

We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by $k$-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fideli...