<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.</p></abstract>

In this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.

Thermal Fluctuations in Electric Circuits and the Brownian Motion

Department of Physics, Faculty of Electrotechnics and Informatics, Technical University of Košice, Park Komenského 2, 042 00 Košice, Slovakia

Department of Mathematics and Physics, Institute of Humanitarian and Technological Sciences, The University of Security Management, Kukučínova 17, 040 01 Košice, Slovakia

Journal of Electrical Engineering

{"article-title":"Thermal Fluctuations in Electric Circuits and the Brownian Motion"}

In this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations...

Thermal Fluctuations in Electric Circuits and the Brownian Motion

Published Online: Jun 07, 2011

Page range: 252 - 256

DOI: https://doi.org/10.2478/v10187-010-0036-1

Keywords
electric circuits, thermal fluctuations, Brownian motion, optical trap, generalized Langevin equation

This content is open access.

Thermal Fluctuations in Electric Circuits and the Brownian Motion

Published Online: Jun 07, 2011

Page range: 252 - 256

DOI: https://doi.org/10.2478/v10187-010-0036-1

Keywordselectric circuits, thermal fluctuations, Brownian motion, optical trap, generalized Langevin equation

This content is open access.

Keywords
electric circuits, thermal fluctuations, Brownian motion, optical trap, generalized Langevin equation