Statistical Physics of Many-Particle Systems

Albert Thomas Fromhold

Yoshifumi Ito

In this paper, we study the phenomena of the system of free particles on the view point of natural statistical physics. Thereby we derive the Schrödinger equation of this physical system and solve the initial value problem of this Schrödinger equation. Thereby we obtain the structure of this physical system at the stationary state. Thus we obtain the information of the natural statistical distribution of the position variable and the momentum variable of this physical system.

Yoshifumi Ito

In this paper, we study the phenomena of potential well of infinite depth on the view point of natural statistical physics. The mathematical model of this physical system is the system of micro-particles moving periodically with constant velocity in the interval D = [−a, a], (a > 0). Thereby we obtain the structure of this physical system at the stationary state. Thus we clarify that this physical system is the composed state of the proper physical systems at the stationary state and the ratio of their composition is given by the sequence {|an|2}n=0 ∪ {|bn|2}∞n=1, where an, (n ≥ 0) and bn, (n ≥ 1) are the Fourier type coefficients of the initial state ψ ∈ L2. Then we obtain the energy expectation of the total physical system Ē =∞Σn=0 n2π2ℏ2/2ma2 (|an|2 + |bn|2), where m denotes the mass of one micro-particle.

W. D. Kraeft, D. Kremp, W. Ebeling +1 more

Stephen J. Gustafson, Israel Michael Sigal

Dragoş-Victor Anghel

After a very brief introduction to the concept of fractional exclusion statistics (FES), introduced by Haldane in Phys. Rev. Lett. 67, 937 (1991), I shall present some recent results regarding the basic properties of this statistics. These properties have been overlooked for almost two decades and because of that, the application of FES to concrete physical systems was, to a certain degree, arbitrary. Essentially, the FES is a generalization of the Pauli Exclusion Principle which allows one to describe systems of interacting particles (bosons or fermions) as systems of ideal particles, but which obey a more peculiar type of statistics. In the second part of the paper I shall present some application of FES by analyzing concrete systems of interacting particles.