Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 43: Einstein Symposium Brownian Motion, Diffusion and Beyond (SYBM) – Contributed Talks I
DY 43.3: Vortrag
Dienstag, 8. März 2005, 15:00–15:15, TU H2032
On the quantum description of Einstein’s Brownian motion — •Bassano Vacchini1 and Francesco Petruccione2 — 1Universita degli Studi di Milano, Italy — 2University of KwaZulu-Natal, South Africa
A fully quantum treatment of Einstein’s Brownian motion is given, showing the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature of the medium. The former leads to a clearcut relationship with Holevo’s result on translation-covariant quantum-dynamical semigroups, the latter to a formulation of the fluctuation-dissipation theorem in terms of the dynamic structure factor, a two-point correlation function introduced in seminal work by van Hove, directly related to density fluctuations in the medium and therefore to its atomistic, discrete nature. A microphysical expression for the generally temperature dependent friction coefficient is given. A comparison with the Caldeira Leggett model is drawn.
F. Petruccione and B. Vacchini, quant-ph/0411089; B. Vacchini, Phys. Rev. Lett. 84, p. 1374 (2000); J. Math. Phys. 42, p. 4291 (2001); Phys. Rev. E 66, 027107 (2002)