Quantum theory: the role of microsystems and macrosystems

Lanz, L.; Vacchini, Bassano; Melsheimer, O.

doi:10.1088/1751-8113/40/12/s14

Cited by 6 publications

(6 citation statements)

References 46 publications

(56 reference statements)

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“…In particular the analysis of the interaction of a quantum system with a structured reservoir, performed via a time-convolutionless projection operator technique relying on the use of correlated projection operators adapted to the structured reservoir [7], has led to point out a generalized Lindblad structure [8]. This generalized Lindblad structure describes a non-Markovian dynamics on states which are given by classical convex mixtures of subcollections, that is positive trace class operators with trace equal or less than one, naturally appearing in the description of quantum experiments [9]. Master equations of this form have already been proposed in an utterly different context in order to introduce the notion of event in the description of quantum mechanical systems [10], for the purpose of better understanding the interplay between classical and quantum description of physical reality.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian dynamics for bipartite systems

Vacchini

2008

Phys. Rev. A

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We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which we term quantum Bloch-Boltzmann equation, is derived, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom is amenable to a classical treatment and not resolved in the final measurement, though relevant for the interaction with the reservoir, non-Markovian behaviors such as stretched exponential or power law decay of coherences can be put into evidence.Comment: published version, 15 pages, revtex, no figure

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Section: Introductionmentioning

confidence: 99%

Non-Markovian dynamics for bipartite systems

Vacchini

2008

Phys. Rev. A

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“…[3][4][5][6][7][8][9][10]), to which we refer the reader for more rigorous and detailed presentations. A more concise account of similar ideas has also been given in [11].…”

Section: Quantum Mechanics As Quantum Probabilitymentioning

confidence: 91%

Theoretical Foundations of Quantum Information Processing and Communication

Brüning¹,

Petruccione²

2010

Lecture Notes in Physics

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Summary. The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in view of the related symmetry group, recalling the general structure of mappings covariant under the same group. This is done for damped harmonic oscillator, two-level system and quantum Brownian motion. Special attention is devoted to the general structure of translation-covariant master equations. Within this framework a recently obtained quantum counterpart of the classical linear Boltzmann equation is considered, as well as a general theoretical framework for the description of different decoherence experiments, pointing to a connection between different possible behaviours in the description of decoherence and the characteristic functions of classical Lévy processes.

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“…[3][4][5][6][7][8][9][10]), to which we refer the reader for more rigorous and detailed presentations. A more concise account of similar ideas has also been given in [11].…”

Section: Quantum Mechanics As Quantum Probabilitymentioning

confidence: 91%

“…Such a condition typically applies when a symmetry, available in the system one is studying, is not spoiled by the transformations brought about on the system by letting it interact with another system, be it a reservoir or a measuring apparatus. The possibility of giving a general solution of the covariance equation (11) obviously depends on the unitary representation of the group and on the class of mappings considered, possibly giving very detailed information on the general structure of such mappings.…”

Section: Covariancementioning

confidence: 99%

Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics

Vacchini

2009

Lecture Notes in Physics

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The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in view of the related symmetry group, recalling the general structure of mappings covariant under the same group. This is done for damped harmonic oscillator, two-level system and quantum Brownian motion. Special attention is devoted to the general structure of translation-covariant master equations. Within this framework a recently obtained quantum counterpart of the classical linear Boltzmann equation is considered, as well as a general theoretical framework for the description of different decoherence experiments, pointing to a connection between different possible behaviours in the description of decoherence and the characteristic functions of classical Lévy processes.

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Quantum theory: the role of microsystems and macrosystems

Cited by 6 publications

References 46 publications

Non-Markovian dynamics for bipartite systems

Non-Markovian dynamics for bipartite systems

Theoretical Foundations of Quantum Information Processing and Communication

Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics

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