Diffusion of Brownian particles in a spatially periodic potential with a finite life-time

  • Ulada A. Vysotskaya Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Irina V. Shapochkina Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Viktor M. Rozenbaum Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, General Naumov Street, 17, 03164, Kiev, Ukraine
  • Leonid I. Trakhtenberg Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street, 4, 119991, Moscow, Russia; Karpov Institute of Physical Chemistry, Obukha Lane, 3, 105064, Moscow, Russia

Abstract

We consider the motion of Brownian particles in a spatially periodic asymmetric potential with a finite life-time. It is assumed that, at the initial time, there is one particle for each period at a certain point. Further, the diffusion in this potential takes place. The problem definition is to calculate the probability density to find a particle in the potential profile considered, which is characterized by a finite life-time. It is shown that the desired quantity is the Laplace transformation of Green’s function of the Smoluchowski equation with certain boundary conditions. The problem is solved for the sawtooth potential profile described by a piecewise-linear function. The explicit analytical expressions have been obtained and the graphic interpretation of the probability density has been presented; the influence of the model parameters (lifetime duration of the potential profile and the relation of its amplitude to thermal energy) on the features of the probability density has been analyzed. We also discuss the application of the results obtained to calculations of the characteristics of Brownian motors, which model artificial nano-devices, the systems that can rectify non-equilibrium fluctuations of different nature to the directional motion of particles.

Author Biographies

Ulada A. Vysotskaya, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

student at the faculty of physics

Irina V. Shapochkina, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics), docent; associate professor at the department of computer simulation, faculty of physics

Viktor M. Rozenbaum, Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, General Naumov Street, 17, 03164, Kiev, Ukraine

doctor of science (physics and mathematics), full professor; head of the department of theoretical and experimental physics of nanosystems

Leonid I. Trakhtenberg, Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street, 4, 119991, Moscow, Russia; Karpov Institute of Physical Chemistry, Obukha Lane, 3, 105064, Moscow, Russia

doctor of science (physics and mathematics), full professor; head of the laboratory of functional nano composites, Semenov Institute of Chemical Physics, Russian Academy of Sciences; chief researcher at the laboratory of theory of physical and chemical processes, Karpov Institute of Physical Chemistry

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Published
2017-09-29
Keywords: diffusion dynamics, periodic potential with a finite life-time, Green’s function, Brownian motors
How to Cite
Vysotskaya, U. A., Shapochkina, I. V., Rozenbaum, V. M., & Trakhtenberg, L. I. (2017). Diffusion of Brownian particles in a spatially periodic potential with a finite life-time. Journal of the Belarusian State University. Physics, 3, 33-40. Retrieved from https://journals.bsu.by/index.php/physics/article/view/454
Issue
No 3 (2017): Journal of the Belarusian State University. Physics
Section
Physics of Electromagnetic Phenomena

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