Convergence of the quantum Boltzmann map |
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Authors: | R F Streater |
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Institution: | (1) Bedford College, Regent's Park, NW1 5NS London, England;(2) Present address: Department of Mathematics, Kings College Strand, WC2 R2LS London, England |
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Abstract: | We consider a non-linear map on the space of density matrices, which we call the Boltzmann map . It is the composition of a doubly stochastic mapT on the space ofn-body states, and the conditional expectation onto the one-body space. WhenT is ergodic, then the iterates of take any initial state to the uniform distribution. If the energy levels are equally spaced, andT conserves energy and is ergodic on each energy shell, then iterates of take any initial state of finite energy to a canonical distribution. |
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