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Entropy 2018, 20(2), 123;

Kinetic Energy of a Free Quantum Brownian Particle

Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
Author to whom correspondence should be addressed.
Received: 29 December 2017 / Revised: 21 January 2018 / Accepted: 9 February 2018 / Published: 12 February 2018
(This article belongs to the Special Issue Theoretical Aspect of Nonlinear Statistical Physics)
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We consider a paradigmatic model of a quantum Brownian particle coupled to a thermostat consisting of harmonic oscillators. In the framework of a generalized Langevin equation, the memory (damping) kernel is assumed to be in the form of exponentially-decaying oscillations. We discuss a quantum counterpart of the equipartition energy theorem for a free Brownian particle in a thermal equilibrium state. We conclude that the average kinetic energy of the Brownian particle is equal to thermally-averaged kinetic energy per one degree of freedom of oscillators of the environment, additionally averaged over all possible oscillators’ frequencies distributed according to some probability density in which details of the particle-environment interaction are present via the parameters of the damping kernel. View Full-Text
Keywords: quantum Brownian motion; kinetic energy; equipartition theorem quantum Brownian motion; kinetic energy; equipartition theorem

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Bialas, P.; Łuczka, J. Kinetic Energy of a Free Quantum Brownian Particle. Entropy 2018, 20, 123.

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