Hirotsugu Matsuda

Theory of Normal Vibrations of Chain Molecules with Finite Length

This paper is concerned in the end effects on the normal vibrations of a chain molecule with finite length. In Part I we study the mathematical problem of how to solve the eigenvalue problem of the GF matrix of the chain molecule with finite length. Making use of the fact that the force range can be regarded finite we reduce the problem to solving a determinantal equation usually of much lower order than that of the GF matrix through the introduction of auxiliary variables and transfer matrices. We obtain the simple formula for giving an admissible phase difference in which the end effect is taken into account. In Part II, using this formula we analyze the infrared data of Snyder on crystalline normal paraffins C3H8 through C30H62. Our analyses indicate that the formula is generally useful for making extrapolation, interpolation, assignment, and determination of frequency‐phase relations from the experimental data of homologous series of chain molecules.

The Effect of Interatomic Potential on the Feature of Solid-Liquid Phase Transition

Most substances in nature are in the solid state at low temperatures, and the solid undergoes a solid-liquid phase transition at a certain temperature under given pressure. The features of solid-liquid phase transitions of various substances should be a reflection of the nature of the interatomic potential, and the purpose of this article is to give a brief review of some recent work carried out with the aim of elucidating the effect which the interatomic potential has on the features of solid-liquid phase transition.

A New Approach to Green's Function of a Particle in One Dimension

The Schrodinger equation of a particle moving in one dimension in a given static potential is solved. The density matrix corresponds to a Laplace transform of Greens function and satisfies a diffusion-type equation whlch may be regarded as representing a certain limit of a discrete Markoffian random walk process. The space occupied by the system is divided into nonoverlapping regions; in each, the Sehrodinger equation can be solved. A path concept is introduced to synthesrze the solutions for the regions and formulate the one- particle Greens function. The energy bands of a one-dimensional infinite system are discussed. The condition for the existence of the impurity band is derived, which qualitatively supports Andersons theory on the absence of diffusion in certain random lattices.

On the Grand Canonical Distribution Method of Statistical Mechanics

Usually, the grand canonical distribution method is derived only through plausibility arguments, and up to the present its accurate proof has never been made basing directly on ergodic theorem. In order to give the method a sound !:ass, we attempt to reformulate this in the case of ordinary classical liquids, and show that it is practically eq~ivalent to both the microcanonical and the canonical distribution methods. As the result, we can safely use any one of the three methods of statistical mechanics, even for the purpose of investigating phase change.

A Lattice Model of Liquid Helium, III Equilibrium Properties of Liquid He4 and Mixtures of He4 and He3

The partition function of the lattice model of liquid He4 developed in the preceding papersll,Zl is shown to be derived by determining the form of a universal function of one variable so far as one admits three assumptions previously made. Instead of determining the function by using Kikuchis approximation as before, the determination is made here by making use of the experimental values of heat capacity at various temperatures under saturated vapour pressure together with two other thermodynamical data at the ,\-point. Comparison of the values thus derived with experimental ones is made for various thermodynamical quantities of pure liquid He4 and of mixtures of He4 and He3. The agreements are good, and a consistent explanation of various peculiar properties of this liquid is obtained.

WITHDRAWN: Structure of the Spectra of Disordered Systems. I: —– Fundamental Theorems —–

Two theorems are presented, which play a fundamental role in discussing the spectra of disordered systems. The first theorem is valid for any mixed lattice which is described by a set of a number of 2x2 non-singular transfer-matrices with real traces, arranged regularly or randomly. It states that, if a value of frequency or energy lies in one of the spectral gaps for every constituent regular lattice, and if the fixed points of the transformations induced by these matrices are so arranged that there exists a trapping region, the density of frequency- or energy-spectrum of the mixed lattice vanishes at this frequency or energy-value. For some special forms of the transfer-matrices, which often appear in physical problems, the latter condition may be stated in terms of a simple notion “phase”, so that we get the second theorem. Various theorems of Saxon-Hutner-type are to be deduced from these theorems, according to the nature, or the manner of description, of individual systems.