Geodesic
Heat flux structure for Ornstein--Uhlenbeck particles of a one-dimensional harmonic chain
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 180-193.

Voir la notice de l'article provenant de la source Math-Net.Ru

A one-dimensional harmonic chain of $N$ particles is considered, located between two thermal reservoirs (Ornstein–Uhlenbeck particles). An exact solution is constructed for the system of equations describing the dynamics of the system. On the basis of this solution, an analytical expression is obtained for the discrete expression of the heat flux of the model under study, when the time $t \to \infty$, which corresponds to the consideration of stationary transport conditions. It is shown that the heat flux includes two physically different components. The first of them is proportional to the temperature difference between the reservoirs and characterizes the heat transfer along the chain. The second determines the initial value of the flow when the temperatures of the tanks are equal. 
@article{DVMG_2021_21_2_a4,
     author = {M. A. Guzev and A. V. Gorbunov},
     title = {Heat flux structure for {Ornstein--Uhlenbeck} particles of a one-dimensional harmonic chain},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {180--193},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a4/}
}
TY  - JOUR
AU  - M. A. Guzev
AU  - A. V. Gorbunov
TI  - Heat flux structure for Ornstein--Uhlenbeck particles of a one-dimensional harmonic chain
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2021
SP  - 180
EP  - 193
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a4/
LA  - ru
ID  - DVMG_2021_21_2_a4
ER  - 
%0 Journal Article
%A M. A. Guzev
%A A. V. Gorbunov
%T Heat flux structure for Ornstein--Uhlenbeck particles of a one-dimensional harmonic chain
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2021
%P 180-193
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a4/
%G ru
%F DVMG_2021_21_2_a4
M. A. Guzev; A. V. Gorbunov. Heat flux structure for Ornstein--Uhlenbeck particles of a one-dimensional harmonic chain. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 180-193. http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a4/

[1] M. A. Guzev, A. A. Dmitriev, “Teplovoi potok v modeli Lanzhevena dlya dvukh chastits”, Dalnevostochnyi matem. zhurnal, 21:1 (2021), 39–44 | DOI | MR | Zbl

[2] B. Luis, “Active Ornstein-Uhlenbeck particles”, Physical Review E, 100 (2019) | DOI

[3] S. Lepri, R. Livi, A. Politi, “Thermal conduction in classical low-dimensional lattices”, Physics Reports, 377 (2003), 1-—80 | DOI

[4] 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 | DOI | Zbl

[5] A. Dhar, R. Dandekar, “Heat transport and current fluctuations in harmonic crystals”, Physica A: Statistical Mechanics and its Applications, 418 (2015), 49–64 | DOI | Zbl

[6] M. A. Guzev, A. A. Dmitriev, “Razlichnye formy predstavleniya resheniya odnomernoi garmonicheskoi modeli kristalla”, Dalnevostochnyi matem. zhurnal, 17:1 (2017), 30–47 | MR | Zbl