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arXiv · 0812.4108

Non-Equilibrium Dynamics of Dyson's Model with an Infinite Number of Particles

Makoto Katori·Hideki Tanemura
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Abstract

Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant $β/2$. We give sufficient conditions for initial configurations so that Dyson's model with $β=2$ and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of $\Z$ is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.

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Makoto Katori, Hideki Tanemura. 2009-06-19. Non-Equilibrium Dynamics of Dyson's Model with an Infinite Number of Particles. https://doi.org/10.1007/s00220-009-0912-3

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