Pathria's approach has been used to deal with the properties of the finite cubic system of 4He under constant pressure. The analytic expressions for the total number of particles N and the total pressure p near the critical point are obtained for mixture, antiperiodic, Neumann, and periodic boundary conditions. Influences of various boundary conditions upon low-temperature and critical characters of finite systems are discussed. For five boundary conditions, the relationship between the superfluid transition temperature T' and the size of the finite system Lo has been obtained. The results of this paper can be used in the case of superconductivity. Besides, from this work and others, we have obtained the formula for the phase-transition temperature T' in a finite system, t=σLo-b; here b is described as the finiteness constant, and σ is determined by the boundary conditions, the properties of the system, and the interaction between the system and the walls of the container.

We propose an electronic liquid model of superconductivity. We assume that in a crystal most of the movable electrons are in the liquid phase. Applying the quasi-crystal lattice model of a liquid and Toda's potential, we derive the existence of solitary waves of electron, pairs described by a GL equation. From this, superconduetivity, Josephson effect and Meissner effect can be proved. We then derive an approximate formula for Tc.

In metals and compounds there exist small regions in which the phases of electron-pair waves are coherent. These regions are called superconducting domains (SD). At temperatures lower than Tc, these regions connect with each other and form a superconductor. The electron-pairs are partially bound pairs formed by electromagnetic interactions. Coherence gives rise to solitary waves and the Josephson effect. Ideal conductivity and the Meissner effect follow from these. The different effects of lattice vibrations on low and high-Tc superconductors are explained as well.

This paper studies the effects of changes of three parameters on the gap and the pseudogap: the antiferromagnetic short-range coherence length, the hopping integral, and the dielectric constant, and explains the results from three kinds of corresponding experiments.

A unified model of the superconducting mechanism has been put forward. The model suits not only to high-Tc but also to low-Tc superconductors. It is found that there are superconducting domains (SD) in crystal. When T≤Tc, all the SD's in the whole crystal are connected with one another. We have obtained the formula of Tc. On the basis of theformula and theory of quantum mechanics, the different behaviours of isotopic effects in low-and high-Tc superconductors as well as C60, the triangular peak of Tc of transition metals, Matthias rules, and other effects are explained. New superconductors with higher Tc are predicted.