Far Eastern Mathematical Journal

To content of the issue


Heat flux in the Langevin model for two particles


Guzev M.A., Dmitriev A.A.

2021, issue 1, Ñ. 39-44
DOI: https://doi.org/10.47910/FEMJ202103


Abstract
The analytical representation for the heat flux is obtained on the basis of the constructed solution in a one-dimensional harmonic model for two particles. At $t\rightarrow\infty$, the amplitude asymptotic behavior of the flow passing through the particle is shown to be determined by the temperature difference between the left and right heat reservoirs, between which the system is located. The dynamic behavior of the thermal characteristic is oscillating in time; its oscillation period is set by the parameter of the system.

Keywords:
the Langevin model, heat flux, particle system

Download the article (PDF-file)

References

[1] G. E. Uhlenbeck, L. S. Ornstein, “On the Theory of the Brownian Motion”, Phys. Rev., 36 (1930), 823–841.
[2] S. Lepri, R. Livi, A. Politi, “Thermal conduction in classical low-dimensional lattices”, Physics Reports, 377 (2003), 1–80.
[3] F. Bonetto, J. L. Lebowitz, J. Lukkarinen, “Fourier’s Law for a Harmonic Crystal with Self-Consistent Stochastic Reservoirs”, Journal of Statistical Physics, 116 (2004), 783–813.
[4] A. Dhar, R. Dandekar, “Heat transport and current fluctuations in harmonic crystals”, Physica A: Statistical Mechanics and its Applications, 418 (2015), 49–64.
[5] A.M. Krivtsov, “ Rasprostranenie tepla v beskonechnom odnomernom garmonicheskom kristalle” , DAN, 464:2 (2015), 162–166.
[6] M. A. Guzev, A. A. Dmitriev, “ Ostsilliatsionno-zatukhaiushchee povedenie temperatury v kristalle”, Dal'nevostochnyi matem. zhurnal, 17:2 (2017), 170–179.

To content of the issue