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International Journal of Modern Physics B

Quantum Friction: A Bell Path Integral Study

Luiz C. L. Botelho, Edson P. da Silva

Published Nov 10, 1998• 0 citations
Publisher

Abstract

We write effective propagators associated to: (1) A quantum particle interacting with a classical gas and a quantum bosonic gas, modeling friction environments. (2) A noisy and quantum phonon field modeling friction environment at zero temperature. These studies are implemented by means of the Bell functional integrals representing these external dissipative environments.

DOI
10.1142/s0217979298001678

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We write effective propagators associated to: (1) A quantum particle interacting with a classical gas and a quantum bosonic gas, modeling friction environments. (2) A noisy and quantum phonon field modeling friction environment at zero temperature. These studies are implemented by means of the Bell functional integrals representing these external dissipative environments.
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals the de Broglie momentum of the mean free path divided by the mean free path. Alternatively, the corresponding mobility of the quantum particle in the classical gas is equal to the square of the mean free path divided by the Planck constant. The Brownian motion of a quantum particle in a quantum environment is also discussed.
CONTENTS: Preface Bosonic Path Integrals Nelson's Stochastic Mechanics by Means of Feynman Path Integrals Feymman path-integrals for Brownian Classical Motions (1+1)-dimensional Burger turbulence in the framework of Hopf-Cole Transformation and Feymman Trajectories path-integrals Feynman-Wiener Path Integral Representations for the Quantum Harmonic Oscillator with Time-Dependent Stochastic Frequency: Quantum Brownian Motions and Navier-Stokes Weakly Turbulence Some studies on functional integrals representations for fluid motion with random conditions Statistics turbulence suppression by a strong magnetic field: A Feynman path integral argument A non-linear diffusion equation, Some existence and uniqueness results on weak solutions for random initial conditions and its path integral representation -- a mathematical methods approach The Exact Evalution of the Response Function for Wave Propagation in Random Media: A Functional Integral Approach On the Abstract Method of Integration for Wave Equation and some Applications for Wave Physics Feynman Path-Integral Studies for Quantum Particles Propagators Interacting with Environments The Quantum Fractional Dimensional Brownian Motion: A Path-Integral Study Ohm's Law: A Langevin Path-Integral Study at Classical and Quantum W.K.B. Regime On the Statistical of An Ideal Gas with Mass Fluctuations and the Boltzman Ergodic Theorem: The Combined Boltzman-Tsallis Statistics The Suppression of the Quantum Phenomena by an External Strong White-Noise Magnetic Field: A Path Integral Argument Index.
We write in terms of path integrals the effective quantum propagator associated to a quantum particle interacting with a fractional-dimensional reservoir modelled by a scalar and vectorial phonon field in a space-time R v , with v an arbitrary real number. We show, thus, that the classical regime related to this quantum-fractional-dimensional Brownian particle motion is given by the fractional Langevin equation (a fractional time diffusion process). As a consequence, we deduce from first (microscopic) principles fractional-dimensional diffusion phenomena.