Construction of dynamics in one-dimensional systems of statistical mechanics

E. T. Y. Hsieh

Nikolay N. Bogolubov

Gene Lamm

An alternative to the standard Metropolis-based approach for evaluating quantum statistical mechanical ensemble averages is introduced. The method is based on the close similarity between the Bloch equation and the Smoluchowski diffusion equation. Stochastic ‘‘Bloch trajectories’’ are constructed from local solutions to the Bloch equation for the density matrix and used to evaluate Boltzmann ensemble averages and partition functions. This is analogous to the use of Brownian dynamics trajectories in diffusion calculations. Sample results for selected one-dimensional systems are presented and the extension to multidimensional problems is discussed.

Yoshimasa Kurihara, Khiem Hong Phan, Nhi My Uyen Quach

On the basis of the theory of thermodynamics, a new formalism of classical nonrelativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on a (1+n)-dimensional smooth manifold are geometrically treated as dynamical variables. The statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationship between classical and quantum mechanics is discussed from the viewpoint of statistical mechanics. The maximum-entropy principle is shown to provide a unified view of both classical and quantum mechanics.

Derek W. Robinson

Mitsuyoshi Tomiya, Shoichi Sakamoto, Naotaka Yoshinaga

この論文は国立情報学研究所の電子図書館事業により電子化されました。