Low-energy effective theory of far-from-equilibrium time-evolving Bose systems

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At very low energies and high phase-space densities, the wave nature of matter is a key to understanding the collective quantum dynamics of interacting many-particle systems. In this regime, which can be realized in systems as different as cold atomic gases or (hypothetical) dark-matter halos, a quantum field theoretical description is required. Theories formulated in terms of the fundamental field degrees of freedom, e.g., the Bose field of a cold-atom gas, typically need to be evaluated in highly non-perturbative approximations to account for the concomitant strong correlations. In that low-energy regime, however, collective matter-wave dynamics prevails and this is encoded mainly in the coherence of the phase of the quantum field. The phase “lives” on a circle rather than in the cartesian coordinate system of the real and imaginary parts. Low-energy effective models taking this into account represent a useful alternative approach to descriptions in terms of fundamental fields, as they can describe the correlations of interest already in perturbative approximations, which are easier to evaluate. Here we consider strong correlations which are caused by non-linear excitations such as ensembles of topological defects and other, less ordered excitations of the quantum phase and density degrees of freedom. The central goal of this project is to develop low-energy effective field models to be used for describing dynamics far from equilibrium. The emphasis will be set on single- and multicomponent ultra cold Bose gases. Building on preliminary work for U(N) symmetric systems with strong phase excitations we will apply our methods to different models. This will include descriptions of defect-bearing Bose gases obtained through duality transformations. The latter lead to a statistical formulation of the dynamics which allows the computation of field correlations without tracing the kinematics of single defects in the system. A further goal of this project is to develop a variational statistical approach to far-from-equilibrium systems universally scaling in space and time, yielding their correlations by approximative maximization of a Rényi entropy of information. The main goal is to identify the relation between this approach, closely connected to Tsallis' non-extensive thermostatistics, and the determination of scaling solutions from kinetic equations. Our goals are highly relevant in view of the still many open questions in the realm of far-from-equilibrium dynamics and the thermalization or equilibration of quantum systems.