Hydrodynamic limit for a spin system on a multidimensional lattice |
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Authors: | Yuki suzuki Kôhei Uchiyama |
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Institution: | (1) Department of Mathematics, Faculty of Science and Technology, Keio University, 223 Hiyoshi Yokohama, Japan;(2) Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, 152 Meguro Tokyo, Japan |
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Abstract: | Summary The hydrodynamic limit for a Markov process of 0, )-valued spin fields on a periodic multidimensional lattice is studied. In the process a positive real number, called energy, is attached to each site of the lattice and each couple of adjacent sites exchange thier energy by random amounts at random times. The law of the exchange is such that the sum of the total energy is conserved, and that the process is reversible and of gradient type for the energy distribution. We show that under diffusion type scaling of space and time, the macroscopic energy distribution converges to a deterministic limit which is characterized by a non-linear diffusion equation /t=2–1P(), whereP is an increasing function which in a typical case equals const·2. |
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Keywords: | 60K35 82A50 |
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