GENERAL QUESTIONS OF THERMODYNAMICS, STATISTICAL PHYSICS, AND QUANTUM MECHANICS

The low-energy spectrum and low-temperature thermodynamic properties of a one-dimensional lattice electron system with long-range interelectron repulsion are studied at an arbitrary electron filling factor, c(e). It is established that the value of the gap in this spectrum is an oscillating function of the inverse filling factor. This value tends to zero at c(e) = 1/q (q = 1, 2 ...) reaching the maximum at c(e) = 2/(2q + 1). It is shown that the low-energy spectrum of the system under consideration can be described in terms of one-dimensional structures which are analogs of the domains in one-dimensional spin systems. The question about the decay of these "domains" is considered. The method of modified transfer-matrices is proposed for the investigation of thermodynamic properties of such systems. It is shown that increasing the number of interacting electrons leads to the appearance of more and more fine "stairs" in the low-temperature dependence of the chemical potential on the electron density. The influence of a disorder in host-lattice site positions on the thermodynamic characteristics of the system is considered. It is established that the disorder destroys the "stairs".