1,721,065 research outputs found
Master-equations for the study of decoherence
No full textDifferent structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator of a quantum dynamical semigroup in presence of translation invariance recently found by Holevo
Dissipative systems and objective description : quantum Brownian motion as an example
No full textA structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to go over to a Fokker–Planck equation for the description of Brownian motion at quantum level in the long wavelength limit. The structure of this Fokker–Planck equation is expressed in this paper in terms of superoperators, giving explicit expressions for the coefficient of diffusion in momentum in correspondence with two cases of interest for the interaction potential. This Fokker–Planck equation gives an example of a physically motivated generator of quantum dynamical semigroup, which serves as a starting point for the theory of measurement continuous in time, allowing for the introduction of trajectories in quantum mechanics. This theory has in fact already been applied to the problem of Brownian motion referring to similar phenomenological structures obtained only on the basis of mathematical requirements
On the precise connection between the GRW master-equation and master-equations for the description of decoherence
No full textWe point out that the celebrated GRW master equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master equations. Such master equations are typically used for the description of decoherence due to momentum transfers between the system and environment. Building on this analogy we show the exact relationship between the GRW master equation and decoherence master equations, further providing a collisional decoherence model formally equivalent to the GRW master equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications
A classical appraisal of quantum definitions of non-Markovian dynamics
No full textWe consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behavior is analyzed in detail for quantum dynamics which can be built taking as input a class of classical processes
Non-Markovian dynamics for bipartite systems
No full textWe 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
Brownian motion : the quantum perspective
No full textWe briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between the dynamics of the particle and dynamic structure factor of the medium
General structure of quantum collisional models
No full textWe point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely positive maps, a completely positive trace preserving transformation and a waiting time distribution characterizing a renewal process. The relationship between this construction and a Lindblad dynamics is clarified by expressing the solution of a Lindblad master equation in terms of demixtures over different stochastic trajectories for the statistical operator weighted by suitable probabilities on the trajectory space
Non-Abelian linear Boltzmann equation and quantum correction to Kramers and Smoluchowski equation
Full text linkA quantum linear Boltzmann equation, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with, is proposed. Due to this operator structure it is a non-Abelian linear Boltzmann equation and when expressed through the Wigner function it allows for a direct comparison with the classical one. Considering a Brownian particle, the corresponding Fokker-Planck equation is obtained in a most direct way taking the limit of small energy and momentum transfer. A typical quantum correction to the Kramers equation thus appears, describing diffusion in position and further implying a correction to Einstein's diffusion coefficient in the high temperature and friction limit in which the Smoluchowski equation emerges
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