Katsuhiko Nagano

Reduced Equations of Motion for Generalized Fluxes and Forces in the Continued-Fraction Expansion

With the aid of Moris projection operator method, it is shown that the mechanical equations of motion for flux variables can be transformed rigorously into the reduced form da, (t) / dt=iliJr a1 (t)- J: ds [,P1 (t-s) + ¢1 (t-s)] · a1 (s) + g1 (t) + jj(t), where a, (t) is a column matrix of generalized fluxes standing for the j·th order time derivative of the column matrix of state variables a, (t), <Po (t) =0, g0 (t) =0 and liJ1 is a frequency matrix. jj(t) is Moris j·th order random force and ¢1 (t) is the corresponding memory matrix. A new fluctuating force g1 (t) and the corresponding memory matrix cf;1 (t) represent the effects of lower· order fluxes. The temporal behaviour of g 1 (t) is quite different from that of jj(t), and the Laplace transform of cf;1 (t) is represented by an inverted continued fraction of finite order whose poles are all purely imaginary. The Laplace transform of time· correlation matrices of a1 (t) and a. (0) are given in terms of these memory·spectrum matrices cf;1 [z] and ¢1 [z].

Sound Attenuation in Two-Dimensional Magnetic Systems

The sound attenuation constant is calculated for the two-dimensional ferro- and antiferro-magnets. Its frequency and angular dependence turn out to be ω k 2 ln(1/ω k ) and cos 4 θ, respectively. The effect of the uniaxial anisotropy is also taken into account in a self-consistent way.

Sound attenuation in one-dimensional magnetic systems at finite temperatures

Abstract Sound attenuattion constants are calculated for the one-dimensional ferro- and antiferromagnetic systems at finite temperatures. Their frequency dependences, in both cases, turn out to be ω 3 2 k if ω k ⪢ ω c and ω 2 k if ω k ⪡ω c , where ωc is a “cut-off” frequency related to the three-dimensional anisotropic interactions.

Sound Attenuation in One-Dimensional Magnetic Systems

The sound attenuation constant is calculated for the one-dimensional ferromagnet. Its frequency and angular dependence turn out to be ω k 3/2 and cos 4 θ, respectively. The effect of the uniaxial anisotropy is also taken into account in a self-consistent way.

NMR line shapes in low-dimensional magnets

Abstract The NMR line width is calculated for the one- and two-dimensional ferro- and antiferro-magnets in the high temperature region. The NMR line shape turns out to have a structure with double peaks which is quite different from the Lorentzian and the Gaussian type.

Anomalous relaxation in low-dimensional magnets

Abstract Anomalies of the angle-dependent EPR line spectrum and its satellites due to the long-time tails in one- and two-dimensional Heisenberg paramagnets are treated in the high-temperature limit by making use of a new mode-coupling theory. Its numerical results are compared with experimental data for TMMC and (C 2 H 5 NH 3 ) 2 MnCl 4 .

NMR line shape in one-dimensional magnet in the finite temperature region

Abstract The NMR line width is calculated for the one-dimensional ferro- and antiferro-magnets in the finite temperature region. The NMR line shape turns out to have a structure with double peaks which is quite different from the Lorentzian and the Gaussian type.

Heisenberg Linear Chain Magnets with Unlike Spins –An Exactly Soluble Model–

The free energy, susceptibility and correlation functions for a linear chain of N +1 spins with unequal nearest-neighbor isotropic Heisenberg couplings due to two unlike spins randomly distributed on the chain are calculated explicitly in the (classical) limit of infinite spin. The temperature and concentration dependence of susceptibility are given in comparison with that for one-component systems.