Sebastian Fortin

A general theoretical framework for decoherence in open and closed systems

A general theoretical framework for decoherence is proposed, which encompasses formalisms originally devised to deal just with open or closed systems. The conditions for decoherence are clearly stated and the relaxation and decoherence times are compared. Finally, the spin-bath model is developed in detail from the new perspective.

Suppression of decoherence in a generalization of the spin-bath model

The works on decoherence due to spin baths usually agree in studying a one-spin system in interaction with a large spin bath. In this paper we generalize those models by analyzing a many-spin system and by studying decoherence or its suppression in function of the relation between the numbers of spins of the system and the bath. This model may help to identify clusters of particles unaffected by decoherence, which, as a consequence, can be used to store quantum information.

Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.

Compatibility between environment-induced decoherence and the modal-Hamiltonian interpretation of quantum mechanics

Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems, but since its actualization rule applies to closed systems, it seems to stand at odds with EID. The purpose of this article is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the “pointer basis”) are the eigenvectors of an actual-valued observable belonging to the preferred context selected by the MHI.

The problem of identifying the system and the environment in the phenomenon of decoherence

The term “decoherence” generally refers to the quantum process that supposedly turns a pure state into a mixed state, which is diagonal in a well-defined basis. The orthodox explanation of the phenomenon is given by the so-called environment-induced decoherence (EID) approach (Zurek 1982, 1993, 2003; Paz and Zurek 2002), according to which decoherence results from the interaction of an open quantum system and its environment. The study of different physical models shows that, under certain circumstances, the reduced state of the open system rapidly diagonalizes in a basis that identifies the candidates for classical states. By contrast to non-dissipative accounts to decoherence, the EID approach is commonly understood as a dissipative approach: “if one believes that classicality is really an emergent property of quantum open systems one may be tempted to conclude that the existence of emergent classicality will always be accompanied by other manifestations of openness such as dissipation of energy into the environment” (Paz and Zurek 2002, 6).

Predicting Decoherence in Discrete Models

The general aim of this paper is to supply a method to decide whether a discrete system decoheres or not, and under what conditions decoherence occurs, with no need of appealing to computer simulations to obtain the time evolution of the reduced state. In particular, a lemma is presented as the core of the method.

NEW BASES FOR A GENERAL DEFINITION FOR THE MOVING PREFERRED BASIS

One of the challenges of the Environment-Induced Decoherence (EID) approach is to provide a simple general definition of the moving pointer basis or moving preferred basis. In this paper we prove that the study of the poles that produce the decaying modes in non-unitary evolution, could yield a general definition of the relaxation, the decoherence times, and the moving preferred basis. These are probably the most important concepts in the theory of decoherence, one of the most relevant chapters of theoretical (and also practical) quantum mechanics. As an example we solved the Omnes (or Lee–Friedrich) model using our theory.

Non-Hermitian Hamiltonians in decoherence and equilibrium theory

There are many formalisms to describe quantum decoherence. However, many of them give a non-general and ad hoc definition of ?pointer basis? or ?moving preferred basis? , and this fact is a problem for the decoherence program. In this paper, we will consider quantum systems under a general theoretical framework for decoherence and we will present a tentative definition of the moving preferred basis. These ideas are implemented in a well-known open system model. The obtained decoherence and the relaxation times are defined and compared with those of the literature for the Lee?Friedrichs model.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Quantum physics with non-Hermitian operators?.

A pluralist view about information

Focusing on Shannon information, this article shows that, even on the basis of the same formalism, there may be different interpretations of the concept of information, and that disagreements may be deep enough to lead to very different conclusions about the informational characterization of certain physical situations. On this basis, a pluralist view is argued for, according to which the concept of information is primarily a formal concept that can adopt different interpretations that are not mutually exclusive, but each useful in a different specific context.

A Semiclassical Condition for Chaos Based on Pesin Theorem

A semiclassical method to determine if the classical limit of a quantum system shows a chaotic behavior or not based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow–type model and it is concluded that in the classical limit the dynamics exhibited by its effective Hamiltonian is chaotic.