Next Article in Journal
Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays
Previous Article in Journal
Attraction Controls the Entropy of Fluctuations in Isosceles Triangular Networks
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessFeature PaperArticle
Entropy 2018, 20(2), 123; https://doi.org/10.3390/e20020123

Kinetic Energy of a Free Quantum Brownian Particle

1
Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
2
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 Section Statistical Mechanics)
View Full-Text   |   Download PDF [482 KB, uploaded 14 February 2018]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top