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A simple semiclassical approach to the Kramers' problem (1999)

Chaudhuri, Jyotipratim Ray ; Bag, Bidhan Chandra ; Ray, Deb Shankar

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 111 (1999), S. 10852-10858

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ISSN: 1089-7690

Quelle: AIP Digital Archive

Thema: Physik , Chemie und Pharmazie

Notizen: We show that the Wigner–Leggett–Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temperature, ohmic environment can be identified as a semiclassical version of Kramers' equation. Based on an expansion in powers of (h-dash-bar), we solve this equation to calculate the semiclassical correction to Kramers' rate. © 1999 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.480449

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Digitale Medien

A Semiclassical Theory of a Dissipative Henon—Heiles System (1999)

Bag, Bidhan Chandra ; Ray, Deb Shankar

Springer

Journal of statistical physics 96 (1999), S. 271-302

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ISSN: 1572-9613

Schlagwort(e): dissipative quantum system ; semiclassical approximation ; classical chaos ; Henon–Heiles Hamiltonian

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract A semiclassical theory of a dissipative Henon—Heiles system is proposed. Based on ℏ-scaling of an equation for the evolution of the Wigner quasiprobability distribution function in the presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion, which is expressible in terms of a correlation of stochastic fluctuations of the curvature of the potential due to classical chaos, and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of a quantum operator master equation.