Irregular time dependent perturbations of quantum Hamiltonians

2016/01/20 by Robert, Didier
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1601.05174

Abstract

Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians H(t) when this Hamiltonian is perturbed with a quadratic white noise β K. β is a continuous function in time t, β its time derivative and K is a quadratic Hamiltonian. K is the Weyl quantization of K. For time dependent quadratic Hamiltonians H(t) we recover, under less restrictive assumptions, the results obtained in \citebofu, du.In our approach we use an exact Hermann Kluk formula \citero2 to deduce a Strichartz estimate for the propagator of H(t) + βK. This is applied to obtain local and global well posedness for solutions for non linear Schrödinger equations with an irregular time dependent linear part.

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