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 the damped harmonic oscillator, the 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 behaviors in the description of decoherence and the haracteristic functions of classical Lévy processes.

Covariant mappings for the description of measurement, dissipation and decoherence in quantum mechanics / B. Vacchini (LECTURE NOTES IN PHYSICS). - In: Theoretical foundations of quantum information processing and communication : Selected Topics / [a cura di] E. Brüning, F. Petruccione. - Berlin : Springer, 2010. - ISBN 9783642028700. - pp. 39-77

Covariant mappings for the description of measurement, dissipation and decoherence in quantum mechanics

B. Vacchini
Primo
2010

Abstract

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 the damped harmonic oscillator, the 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 behaviors in the description of decoherence and the haracteristic functions of classical Lévy processes.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Book Part (author)
File in questo prodotto:
File Dimensione Formato  
chp%3A10.1007%2F978-3-642-02871-7_2.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 606.18 kB
Formato Adobe PDF
606.18 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/152483
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 9
social impact