3,812 research outputs found
Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics
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 L\'evy processes.Comment: Comments: 38 pages, to appear in Lecture Notes in Physics,
Springer-Verla
Eigenvalues and Holonomy
We estimate the eigenvalues of connection Laplacians in terms of the
non-triviality of the holonomy.Comment: 9 page
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