Displaying similar documents to “Complete asymptotics for correlations of Laplace integrals in the semi-classical limit”

Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

Journées équations aux dérivées partielles

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We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit Λ ( h ) of the ground state energy of this operator. For Kac’s spin model, Λ ( h ) is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which...

On the eigenvalues of a class of hypo-elliptic operators. IV

Johannes Sjöstrand (1980)

Annales de l'institut Fourier

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Let P be a selfadjoint classical pseudo-differential operator of order > 1 with non-negative principal symbol on a compact manifold. We assume that P is hypoelliptic with loss of one derivative and semibounded from below. Then exp ( - t P ) , t ≥ 0 , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of P is computed. This paper is a continuation of a series of joint works with A. Menikoff.