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Gabriela Vasziová, Jana Tóthová, Lukáš Glod and Vladimír Lisý

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 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.

Open access

Lukáš Glod, Gabriela Vasziová, Jana Tóthová and Vladimír Lisý

Brownian Oscillators Driven by Correlated Noise in a Moving Trap

Brownian oscillator, ie a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the chaotic force driving the particle is correlated in time. The dynamics of the particle is described by the generalized Langevin equation with the inertial term, a coloured noise force, and a memory integral. We consider two kinds of the memory in the system. The first one corresponds to the exponentially correlated noise and in the second case the memory naturally arises within the Navier-Stokes hydrodynamics. Exact analytical solutions are obtained in both the cases using a simple and effective method not applied so far in this kind of problems.

Open access

Lukáš Glod, Gabriela Vasziová, Jana Tóthová and Vladimír Lisý

Field-Driven Brownian Motion of Magnetic Domain Walls

The dynamics of a magnetic domain wall (DW) in a wire is studied. The DW is modeled as a Brownian particle subjected to thermal fluctuations and is characterized by the mass, position and velocity. Its motion is damped by friction, pinned by the irregularities in the material and driven by a constant force due to the external magnetic field. We have obtained the corresponding Langevin equation that contains a white-noise force. The use of an effective method taken from the statistical physics allowed us to convert this stochastic equation into an ordinary differential equation. From its solution the mean square displacement of the DW with other relevant time correlation functions and their spectral densities have been found. The electric current induced by the moving DW is also calculated.