Semi-classical behavior of the spectral function

Semi-Classical Behavior of the Spectral Function

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spe...

Spectral Geometry and the Semi-classical Approach

On the Pointwise Behavior of Semi-Classical Measures

In this paper we concern ourselves with the small h asymptotics of the inner products of the eigenfunctions of a Schr6dinger-type operator with a coherent state. More precisely, let 0~ and E) denote the eigenfunctions and eigenvalues of a Schr6dinger-type operator H~ with discrete spectrum. Let 0(x,~) be a coherent state centered at the point (x, ~) in phase space. We estimate as h --+ 0 the av...

Spectral function at high temperature in the classical approximation

At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the classical field approximation. We use this to introduce a nonperturbative approach to the calculation of finite-temperature spectral functions, employing the classical KMS condition in real time. The method is illustrated for the one-particle spectral function ...

Semi-classical Counting Function with Application to Quantum Current

By adapting methods developed in SV] to the semi-classical situation we obtain a new two-term asymptotic formula for the counting function of eigenvalues of h pseudodiierential operators in the limit as h ! 0. Recent results on clustering of eigenvalues obtained in PP2] follow in Corollary and, as an application, we consider the semi-classical behaviour of the quantum current studied recently i...