Emergence of classicality via decoherence described by Lindblad operators (original) (raw)
Environment-induced decoherence and the transition from quantum to classical
Vistas in Astronomy, 1993
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection (einselection) in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equations we study einselection employing the general strategy of the predictability sieve. Assumptions that are usually made in the discussion of decoherence are critically reexamined along with the "standard lore" to which they lead. Restoration of quantum-classical correspondence in systems that are classically chaotic is discussed. The dynamical second law-it is shown-can be traced to the same phenomena that allow for the restoration of the correspondence principle in decohering chaotic systems (where it is otherwise lost on a very short timescale). Quantum error correction is discussed as an example of an anti-decoherence strategy. Implications of decoherence and einselection for the interpretation of quantum theory are briefly pointed out.
Coherent states: a contemporary panorama
Journal of Physics A-mathematical and Theoretical, 2012
Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schrödinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for
Fortschritte der Physik, 1999
In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a Wigner distribution function which is Gaussian in form is found to depend only on the variance of the distribution function. We give a series of inequalities, relating uncertainty to von Neumann entropy and linear entropy. We analyze the conditions for purity of states and show that for a special choice of the diffusion coefficients, the correlated coherent states (squeezed coherent states) are the only states which remain pure all the time during the evolution of the considered system. These states are also the most stable under evolution in the presence of the environment and play an important role in the description of environment induced decoherence.
The Quantum-Classical Transition in Nonlinear Dynamical Systems
2000
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.
Quantum decoherence and the approach to equilibrium (II
Studies in History and Philosophy of Modern Physics, 2005
In a previous paper . Quantum decoherence and the approach to equilibrium I. Philosophy of Science, 70, 330-358] we discussed a recent proposal by Albert [(2000). Time and chance. Cambridge, MA: Harvard University Press. Chapter 7] to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the quantum state of [Ghirardi, G, Rimini, A and Weber, T., (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review, D 34, 470-479]. We proposed an alternative way to explain thermodynamics within no collapse interpretations of quantum mechanics. In this paper some difficulties faced by both approaches are discussed and solved: the spin echo experiments, and the problem of extremely light gases. In these contexts, we point out several ways in which the above quantum mechanical approaches as well as some other classical approaches to the foundations of statistical mechanics may be distinguished experimentally. r
Decoherence: A Closed-System Approach
Brazilian Journal of Physics, 2014
The aim of this paper is to review a new perspective about decoherence, according to which formalisms originally devised to deal just with closed or open systems can be subsumed under a closed-system approach that generalizes the traditional account of the phenomenon. This new viewpoint dissolves certain conceptual difficulties of the orthodox open-system approach but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decoherence, as commonly claimed. Moreover, when the behavior of a decoherent system is described from a closed-system perspective, the account of decoherence turns out to be more general than that supplied by the open-system approach, and the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.
Modern Physics Letters B, 2001
The decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by quantum field theory, rather than by quantum mechanics.
Advances in Physics, 2009
This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions: (i) How can one drive a small dynamical quantum system to behave classically ? (ii) What determines the rate at which two single-particle quantummechanical subsystems become entangled when they interact ? (iii) How does irreversibility occur in quantum systems with few degrees of freedom ? These three questions are posed in the context of the quantum-classical correspondence for dynamical systems with few degrees of freedom, and we accordingly rely on two short-wavelength approximations to quantum mechanics to answer them -the trajectory-based semiclassical approach on one hand, and random matrix theory on the other hand. We construct novel investigative procedures towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. In particular we show how dynamical properties of chaotic classical systems, such as local exponential instability in phase-space, also affects their quantum counterpart. For instance, it is often the case that the fidelity with which a quantum state is reconstructed after an imperfect time-reversal operation decays with the Lyapunov exponent of the corresponding classical dynamics. For not unrelated reasons, but perhaps more surprisingly, the rate at which two interacting quantum subsystems become entangled can also be governed by the subsystem's Lyapunov exponents. Our method allows at each stage in our investigations to differentiate quantum coherent effects -those related to phase interferences -from classical ones -those related to the necessarily extended envelope of quantal wavefunctions. This makes it clear that all occurences of Lyapunov exponents we witness have a classical origin, though they require rather strong decoherence effects to be observed. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with many interacting dynamical systems, going beyond the uncoupled harmonic oscillators model of Caldeira and Leggett.
The Problem of the Classical Limit of Quantum Mechanics and the Role of Self-Induced Decoherence
Foundations of Physics, 2006
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity represented by the limith → 0: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.
Quantum state stability against decoherence
Physics Letters A, 2007
We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson bath temperature, changes depending on the intensity of the classical field.