Self-induced Decoherence Research Articles

Formal Features of a General Theoretical Framework for Decoherence in Open and Closed Systems

Two complementary decoherence formalisms, Environment Induced Decoherence (EID) for open systems and Self Induced Decoherence (SID) for close systems are compared under a common General Theoretical Formalism for Decoherence (GTFD). The differences and similarities of EID and SID are studied, e. g. that the main difference is that EID only considers the relevant information of the proper system S and neglects the rest, while SID considers all possible information available from a certain class of measurement instruments and neglects the non available information.

Growing Classical and Quantum Entropies in the Early Universe

Fil: Ardenghi, Juan Sebastian. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Astronomia y Fisica del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Fisica del Espacio; Argentina

Multi-angle effects in collective supernova neutrino oscillations

We study two-flavor collective neutrino oscillations in the dense-neutrino region above the neutrino sphere in a supernova (SN). The angular dependence of the neutrino-neutrino interaction potential causes ‘multi-angle’ effects that can lead either to complete kinematical decoherence in flavor space or only to small differences between different trajectories. This nonlinear system switches abruptly between ‘self-maintained coherence’ and ‘self-induced decoherence’ among the angular modes, depending on the strength of the deleptonization flux. For a realistic SN the quasi single-angle behavior is probably typical, simplifying the numerical treatment and probably allowing for the survival of observational features of flavor oscillations.

Self-induced decoherence in dense neutrino gases

Dense neutrino gases exhibit collective oscillations where ``self-maintained coherence'' is a characteristic feature, i.e., neutrinos of different energies oscillate with the same frequency. In a nonisotropic gas, however, the flux term of the neutrino-neutrino interaction has the opposite effect of causing kinematical decoherence of neutrinos propagating in different directions, an effect that is at the origin of the ``multiangle behavior'' of neutrinos streaming off a supernova core. We cast the equations of motion in a form where the role of the flux term is manifest. We study in detail the symmetric case of equal neutrino and antineutrino densities where the evolution consists of collective pair conversions (``bipolar oscillations''). A gas of this sort is unstable in that an infinitesimal anisotropy is enough to trigger a runaway towards flavor equipartition. The ``self-maintained coherence'' of a perfectly isotropic gas gives way to ``self-induced decoherence.''

The Problem of the Classical Limit of Quantum Mechanics and the Role of Self-Induced Decoherence

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 limit $$\hbar \rightarrow 0$$ : 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.

The equilibrium limit of the Casati–Prosen model

An alternative explanation of the decoherence in the Casati–Prosen model is presented. It is based on the self-induced decoherence formalism extended to non-integrable systems.

Self-Induced Decoherence and the Classical Limit of Quantum Mechanics

In this paper we argue that the emergence of the classical world from the underlying quantum reality involves two elements: self-induced decoherence and macroscopicity. Self-induced decoherence does not require the openness of the system and its interaction with the environment: a single closed system can decohere when its Hamiltonian has continuous spectrum. We show that, if the system is macroscopic enough, after self-induced decoherence it can be described as an ensemble of classical distributions weighted by their corresponding probabilities. We also argue that classicality is an emergent property that arises when the behavior of the system is described from an observational perspective.

The classical limit of non-integrable quantum systems, a route to quantum chaos

Abstract The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those, which have, as their classical limit, a non-integrable classical system. This quantum systems will be the candidates to be the models of quantum chaos. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

The ``self-induced decoherence'' (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and that (2) this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed ``values'' of measurements. This leads us to question the relevance of SID for treating observed decoherence effects.

Decoherence time in self-induced decoherence

A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian's spectrum. Several decoherence times are estimated: $10^{-13}-$ $10^{-15}s$ for microscopic systems, and $10^{-37}-10^{-39}s$ for macroscopic bodies. For the particular case of a thermal bath, our results agree with those obtained by the einselection (environment-induced decoherence) approach.

Classical limit of non-integrable systems

The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. The decoherence times computed with this approach coincide with those of the literature. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.

Self-induced decoherence: a new approach

According to Zurek, decoherence is a process resulting from the interaction between a quantum system and its environment; this process singles out a preferred set of states, usually called “pointer basis”, that determines which observables will receive definite values. This means that decoherence leads to a sort of selection which precludes all except a small subset of the states in the Hilbert space of the system from behaving in a classical manner: environment-induced-superselection—einselection—is a consequence of the process of decoherence. The aim of this paper is to present a new approach to decoherence, different from the mainstream approach of Zurek and his collaborators. We will argue that this approach offers conceptual advantages over the traditional one when problems of foundations are considered; in particular, from the new perspective, decoherence in closed quantum systems becomes possible and the preferred basis acquires a well founded definition.