Some results on the quantum dynamics of a particle in a Markovian potential

DOI10.1007/BF01229379zbMath0591.60073OpenAlexW1998797819MaRDI QIDQ1074960

Claude-Alain Pillet

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01229379

zbMATH Keywords

evolution equationsemigroupergodicityinvariant measurequantum mechanicslong-time averagemean evolutionunitary propagator

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Transition functions, generators and resolvents (60J35) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items

Markovian repeated interaction quantum systems ⋮ Floquet spectrum for two-level systems in quasiperiodic time-dependent fields ⋮ Diffusive propagation of wave packets in a fluctuating periodic potential ⋮ Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential ⋮ Quantum Brownian motion in a simple model system ⋮ Energy growth in Schrödinger's equation with Markovian forcing ⋮ Random time-dependent quantum walks ⋮ Asymptotic completeness and the absence of bound states in the quantum problem of scattering on a Brownian particle ⋮ Diffusive energy growth in classical and quantum driven oscillators ⋮ Diffusion in the mean for an ergodic Schrödinger equation perturbed by a fluctuating potential ⋮ Ionization of a model atom by perturbations of the potential ⋮ Spectral and stability aspects of quantum chaos ⋮ Correlated Markov quantum walks ⋮ Transport of a quantum particle in a time-dependent white-noise potential ⋮ Diffusion of wave packets in a Markov random potential ⋮ Asymptotic completeness for a quantum particle in a Markovian short range potential ⋮ On the averaged quantum dynamics by white-noise hamiltonians with and without dissipation ⋮ A new spectral analysis of stationary random Schrödinger operators ⋮ Some remarks concerning stability for nonstationary quantum systems.

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