On Heat Reservoirs Composed of Simple Cubic Lattices
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概要
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A rigorous procedure to investigate the effects of heat reservoirs on a time evolution of a system in contact with them is given for a dynamical model, in which two simple "cubic" (1, 2 and 3-dimensional) lattices playing the role of heat reservoirs are attached on both sides of a harmonic chain S. The generalized Langevin equation of Mori for collective motion is used for this purpose. A new non-equilibrium initial ensemble ρ_0, which is considered to represent the basic notion of a heat reservoir, is introduced to interpret the generalized Langevin equation statistically. It is shown that the effects of a one-dimensional (1D) reservoir can be represented by a frictional force and a white-noise-random force experienced by the end particles of the system S, provided that Q=M/m≫1, where n and M are masses of reservoir particles and the end particle of the system S, respectively. In the case of a 3D reservoir there appears, besides these two forces, an extra force which binds the end particles of the system S harmonically to their equilibrium positions. In contrast, it is found that the time-correlation function of the random force associated with 2D reservoir decays much slower and exhibits a sinusoidal behavior asymptotically. From these facts it is concluded that 2D reservoir cannot behave as a source of the white-noise-random force.
- 理論物理学刊行会の論文
- 1972-10-25
著者
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Munakata Toyonori
Department Of Applied Mathematics And Physics Faculty Of Engineering Kyoto University
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MUNAKATA Toyonori
Department of Applied Mathematics and Physics, Faculty of Engineering Kyoto University
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