Quantum Brownian motion and generalizations of Hermite polynomials

DOI10.1016/j.cam.2010.01.051zbMath1252.81087OpenAlexW2084239963MaRDI QIDQ645674

Juan-Miguel Gracia

Publication date: 10 November 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.01.051

zbMATH Keywords

quantum Brownian motionnon-equilibrium momentsequilibrium Wigner functionlowest momentnon-equilibrium Smoluchowski equationsproperties generalized Hermite polynomialsweight of orthogonal generalized Hermite polynomials

Mathematics Subject Classification ID

Brownian motion (60J65) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Quantum stochastic calculus (81S25) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24)

Related Items (1)

Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations

Cites Work

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• Brownian motion, quantum corrections and a generalization of the Hermite polynomials
• Path integral approach to quantum Brownian motion
• The Fokker-Planck equation. Methods of solution and applications.
• On the generators of quantum dynamical semigroups
• Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise
• Brownian motion in a field of force and the diffusion theory of chemical reactions
• Semiclassical Klein–Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential
• On the Quantum Correction For Thermodynamic Equilibrium
• The Statistical Interpretation of Quantum Mechanics
• Brownian motion in a field of force and the diffusion model of chemical reactions
• Quantum noise. A handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics.

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