Abstract
Understanding the non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems that allow reliable theoretical analysis are few and far between. In this paper, we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schrödinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and non-local interactions, and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result, we find that weakly and strongly interacting Bose gases expanding from a parabolic trap can exhibit very similar dynamics.
Highlights
Understanding time evolution of complex quantum systems, often in the presence of strong correlations between constituent particles, is crucial for solving many fundamental problems in physics, from expansion of the early universe, to heavy ion collisions, to pump and probe experiments in solids
While numerous approximate and exact solutions exist for systems in equilibrium, examples of nonequilibrium dynamics of many-body systems that allow reliable theoretical analysis, are few and far between
We used scaling ansatz to show that certain quantum non-equilibrium problems with time-dependent parameters can be related to equilibrium problems with constant parameters provided that the time-dependent parameters satisfy a system of selfconsistency equations
Summary
Understanding time evolution of complex quantum systems, often in the presence of strong correlations between constituent particles, is crucial for solving many fundamental problems in physics, from expansion of the early universe, to heavy ion collisions, to pump and probe experiments in solids. In the context of many-body problems, scaling has first been used within mean-field approaches to bosonic systems, for the classical Gross-Pitaevskii equation [24, 25, 28, 29, 30] Beyond these effective onebody problems, scaling solutions exist for hard-core bosons in one dimension [31] and in the unitary limit of fermionic gases with infinite scattering length [26]; these are problems for which the interaction enters a constraint on the wave function of an otherwise non-interacting system analysis. Further details are given in the Appendices, where we discuss relation of our work to classical integrability of time-dependent bosonic systems with contact interactions
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