Abstract
For a quantum system ofn identical spins of magnitudej, we introduce an integrated density of states of definite total spin angular momentum. The underlying sequence\(\{ \mathbb{K}_n^j :n = 1,2,...\} \) of probability measures satisfies Varadhan's large deviation principle, and converges to a degenerate distribution. We use the Berezin-Lieb Inequalities to obtain upper and lower bounds for the limiting specific free-energy of the spins interacting with a second quantum system under specified conditions on the Hamiltonian. The method is illustrated by applications to the BCS model and to the Dicke maser model.
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Communicated by J. Fröhlich
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Cegła, W., Lewis, J.T. & Raggio, G.A. The free energy of quantum spin systems and large deviations. Commun.Math. Phys. 118, 337–354 (1988). https://doi.org/10.1007/BF01218583
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DOI: https://doi.org/10.1007/BF01218583