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 non-equilibrium environment. To this extent we consider, as key quantity, the overlap between time dependent wavefunctions, that 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 non-equilibrium 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 non-equilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of non-linearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.PACS numbers: 72.10. Pm,05.70.Ln,72.15.Qm Introduction -The response of gapless quantum manybody systems to sudden local perturbations is a remarkably non-linear phenomenon, even a weak disturbance substantially changes the structure of the many-body state. Signatures of this orthogonality catastrophe (OC) emerge in various condensed matter settings [1], from Xray spectra in metals [2] and Luttinger Liquids (LL) [3][4][5][6] to the physics of the Kondo Effect [7][8][9][10][11] and typically results in power-law decays of dynamical correlations. Recently, impressive experimental developments with ultracold atomic gases [12], have made possible to create and probe local excitations in a quantum many-body system with single-site and real-time resolution [13,14], bringing fresh new input to this venerable problem [15]. While most of the attention has been traditionally devoted to perturbations acting on systems in their ground state or, more recently, in driven stationary non-equilibrium conditions [16][17][18][19][20][21][22], much less is known about the response of explicitly time dependent quantum states, such as, for example, those obtained by rapidly changing in time some parameter of an otherwise isolated system. The problem is of current experimental relevance since ultracold gases have proven to be natural laboratories where dynamical quantum correlations can be probed in the time domain. In addition, it also raises a number of intriguing theoretical questions. A coherent time dependent excitation, such as a sudden global quench, creates an effective nonequilibrium time-dependent bath for the local degrees of freedom. What is the effect of such an environment on the OC phenomenon and its associated p...

Transport across an impurity in one-dimensional quantum liquids far from equilibrium

“…It should be noted that there has been a recent spur of interest towards understanding similar dynamical quantum correlations in isolated many body systems excited after quantum quenches [32][33][34][35] . We have considered an example along these lines in a recent work on a time-dependent orthogonality catastrophe problem 36 where we introduced a novel dynamical Loschmidt echo, encoding the response of a highly excited state to a local perturbation. Here we study a similar problem from the point of view of transport.…”

Transient Dynamics ofd-Wave Superconductors after a Sudden Excitation

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Quench-induced entanglement and relaxation dynamics in Luttinger liquids

“…In recent years the LL model has also been proven to be a very powerful tool for studying the dynamics of 1D systems after a quench of the interaction strength. In particular, the subsequent relaxation towards a steady-state and the characterization of the latter has been the focus of many recent works [22,23,[43][44][45][46][47][48][49].…”