On the thermalization of one-dimensional lattices. II. Canonical ensemble

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 $\beta$-Fermi–Pasta–Ulam–Tsingou ($\beta$-FPUT) 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 (PBH) 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.