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| Volume 20 Issue 1 Year 2025 | ||
On the Thermalization of One-Dimensional lattices. II. Canonical Ensemble
Vinogradov G.A.1, Lakhno V.D.2 1Emanuel Institute of Biochemical Physics of RAS, Moscow, Russia Abstract. In this paper we consider the thermalization of one-dimensional lattices in the canonical ensemble. The main methods of thermalization are described, including the Nose–Hoover algorithm and the stochastic Langevin method. The thermalization of lattices with "rigid" symmetric potential β–Fermi–Pasta–Ulam–Tsingou is considered in detail. This example demonstrates the quantitative and qualitative characteristics of the thermalization process. In the next section, the thermalization of a lattice with a "soft'' asymmetric Peyrard–Bishop–Holstein potential is analyzed. Thethermalization of this lattice has some peculiarities related to the kind of Morse potential that models the hydrogen bonds between DNA chains. Finally, the problem of quantum thermalization is mentioned when the quantum character of the vibrational motion of the atoms of the molecular chain is taken into account.
Key words: canonical ensemble, thermalization, Langevin thermostat, β–FPUT and PBH potentials. |
Table of Contents
Original Article
Vinogradov G.A., Lakhno V.D. On the Thermalization of One-Dimensional lattices. II. Canonical Ensemble. Ìàthematical biology and bioinformatics. 2025;20(1):31-46. doi: 10.17537/2025.20.31 (published in Russian) Abstract (rus.) Abstract (eng.) Full text (rus., pdf) References
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