Convergence to equilibrium distribution. The Klein-Gordon equation coupled to a particle |
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Authors: | T. V. Dudnikova |
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Affiliation: | 1.Elektrostal Polytechnical Institute,Elektrostal,Russia |
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Abstract: | The Hamiltonian system formed by a Klein-Gordon vector field and a particle in ℝ3 is considered. The initial data of the system are given by a random function, with finite mean energy density, which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are assumed to be translation invariant. The distribution μ t of the solution at time t ∈ ℝ is studied. The main result is the convergence of μ t to a Gaussian measure as t → ∞, where μ∞ is translation invariant. |
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