Tohru Morita

Statistical Mechanics of Quenched Solid Solutions with Application to Magnetically Dilute Alloys

The arrangement of atoms in solid solutions and alloys, prepared at high temperatures and cooled nonadiabatically, is not the one which is thermodynamically most stable. In establishing theories of phenomena related to the internal degrees of freedom of such a system, such as magnetism, one must be careful to account for this nonequilibrium distribution of atoms. In this paper, systems are treated with the aid of a fictitious equilibrium system. This fictitious system is constructed such that its thermal equilibrium properties are the same as the properties of the non‐thermal‐equilibrium system. Thus one can treat nonequilibrium systems by applying well known thermal equilibrium techniques to the fictitious system. The method is illustrated via the example of a magnetically dilute alloy. Brouts result for a very dilute Ising system is obtained with the aid of the theory of classical fluids, without collecting diagrams. A method for applying the higher approximations developed for classical fluids to the present problem is suggested; calculations and discussions of which are retained for a forthcoming paper.

Derivation of the Generalized Boltzmann Equation in Quantum Statistical Mechanics

The hierarchy of the equations of motion for the reduced density matrices in quantum statistical mechanics is solved and the (cumulant) reduced density matrices at a time t are expressed in terms of those at an earlier time t0. Diagrams are introduced to express the results. With the aid of the technique of partial summations, the general term in the kinetic equation for the one‐particle reduced density matrix or the generalized Boltzmann equation in quantum statistical mechanics is obtained. The equation is non‐Markovian. A method of reducing the equation to Markovian is sketched.

Effect of n‐Spin‐Wave Interaction on the Low‐Temperature Spontaneous Magnetization

For a Heisenberg model of a ferromagnet, it is known that the commutator of the Hamiltonian H and the operator S0− = ΣjSj− is proportional to S0−. From this fact, a conjecture is made on the lowlying energy levels of two‐, three‐, …, n‐spin‐wave problems. With the aid of the conjecture and the assumption that there is no low‐lying n‐spin‐wave bound state, it is concluded that the contributions to the low‐temperature expansion of the spontaneous magnetization due to two‐, three‐, …, n‐spin‐wave problems are of O(T4), O(T13/2), …, O(T5n/2−1), respectively.