A contribution to the statistical mechanics of one-dimensional systems with interactions

Chun Kou Lai

Ya. G. Sinaǐ

Dietmar R. A. Johlen

Xi-Wen Guan, Feng He

In the 60s Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe’s hypothesis for various problems of physics. The works on the lattice gas model, critical behavior in liquid–gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe’s hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.

浩 市村

Russell Davidson, John J. Kozak

In pursuit of the study begun in the preceding paper of the spontaneous emission of a Wigner-Weisskopf atom in a one-dimensional radiation field, the exact solution of this problem in the thermodynamic limit of a system of infinite extent is examined. The analysis reveals the existence in general of three contributions to the probability of the atom's being excited at any moment: a constant contribution and two sorts of time-dependent ones, exponential and nonexponential. For a specific choice of coupling function, this probability is written down in closed form. The link between the constant contribution and the appearance of ghost states and ergodicity is investigated, and criteria given to determine when this contribution does not arise. A numerical study is made of the expressions obtained, and the nonexponential part of the solution compared with approximations for it which have been previously obtained by various means. It is concluded that the predictions of the weak-coupling Prigogine-Résibois master equation are inadequate except when the model is ergodic in a certain sense, and some suggestions are made concerning the relevance of these studies to nonequilibrium statistical mechanics.