title: Transient orthogonality catastrophe in a time-dependent nonequilibrium environment.
abstract: We study the response of a highly excited time-dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient nonequilibrium environment. To this extent we consider, as a key quantity, the overlap between time-dependent wave functions, which we write in terms of a novel two-time correlator generalizing the standard Loschmidt echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through nonequilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one-dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power-law structure even in the presence of a large nonequilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of nonlinearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.
authors.affiliation: Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA; Department of Chemistry, Columbia University, New York, New York 10027, USA; and Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191 Gif-sur-Yvette, France.
authors.forename: Marco
authors.initials: M
authors.lastname: Schiró
authors.affiliation: Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA.
authors.forename: Aditi
authors.initials: A
authors.lastname: Mitra