Irregular time-dependent perturbations of quantum Hamiltonians

  • Didier Robert

    Université de Nantes, France

Abstract

Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time-dependent quantum Hamiltonians when this Hamiltonian is perturbed with a quadratic white noise . is a continuous function in time , its time derivative and is a quadratic Hamiltonian. is the Weyl quantization of .

For time-dependent quadratic Hamiltonians we recover, under less restrictive assumptions, the results obtained in [3, 9, 10]. In our approach we use an exact Herman–Kluk formula [20] to deduce a Strichartz estimate for the propagator of .

This is applied to obtain local and global well posedness for solutions for non-linear Schrödinger equations with an irregular time-dependent linear part.

Cite this article

Didier Robert, Irregular time-dependent perturbations of quantum Hamiltonians. J. Spectr. Theory 6 (2016), no. 4, pp. 955–976

DOI 10.4171/JST/149