Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1103.6188 · Modern Physics Letters A

NEW BASES FOR A GENERAL DEFINITION FOR THE MOVING PREFERRED BASIS

Mario Castagnino, Sebastián Fortín

Published Sep 13, 2011• 18 citations
arXivHTMLPDF

Abstract

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 Omnès (or Lee–Friedrich) model using our theory.

DOI
10.1142/s0217732311036735

Related papers

Defining the moving preferred basis

Mario Castagnino, Sebastián Fortín

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 present a very general definition of the moving preferred basis. In addition, this definition is implemented in a well known model and the time of decoherence and the relaxation time are defined and compared with those of this model.

arXiv:1006.2130•Jun 10, 2010•1 citation

Non-Hermitian Hamiltonians in decoherence and equilibrium theory

Mario Castagnino, Sebastián Fortín

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.

•Oct 1, 2012•11 citations

Non-Hermitian Hamiltonians in decoherence and equilibrium theory

Mario Castagnino, Sebastian Fortin

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'.

arXiv:1304.3190•Journal of Physics A Mathematical and Theoretical•Oct 23, 2012•15 citations

On a possible definition of the moving preferred basis

Mario Castagnino, Sebastián Fortín

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 present a tentative very general definition of the moving preferred basis. which is implemented in a well known open system model. The obtained decoherence and the relaxation times are defined and compared with those of this model.

arXiv:1009.0535•Sep 2, 2010•3 citations

Self-Induced Selection: A New Approach to Quantum Decoherence

Mario Castagnino, Olímpia Lombardi

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.

•Aug 1, 2002•0 citations

Compatibility between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics

Olímpia Lombardi, Juan Sebastián Ardenghi, Sebastián Fortín +1 more

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.

Philosophy of Science•Dec 1, 2011•22 citations
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 Omnès (or Lee–Friedrich) model using our 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 present a very general definition of the moving preferred basis. In addition, this definition is implemented in a well known model and the time of decoherence and the relaxation time are defined and compared with those of this model.
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.
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'.
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 present a tentative very general definition of the moving preferred basis. which is implemented in a well known open system model. The obtained decoherence and the relaxation times are defined and compared with those of this model.
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.
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.