Semiclassical Approach to Spectral Statistics of Interacting Quantum Many-Body Systems

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In recent years, the study of interacting many-body systems has made considerable progress. An improved understanding of many-body localization on the theoretical sideis paired with recent cold-atom experiments allowing the fabrication and the control of interacting many-body systems. To comprehend ever better the dynamics of interacting many-body systems is a central task in many research fields including condensed matter physics, nuclear physics and quantum optics.The aim of this proposal is to characterize the spectral statistics (i.e. spectral correlations) of interacting quantum many-body systems. Understanding the connection between the spectral statistics and the classical dynamics for single-particle systems has been subject of intensive research during the last decades in the research field of quantum chaos. However, for a many-body system new features arise for example due to indistinguishability and the bosonic or fermionic character of the particles. Particularly important for the spectral statistics is also the issue of collective motion as opposed to incoherent motion of the individual particles. A deeper theoretical understanding is difficult as the lines of reasoning developed in quantum chaos cannot simply be carried over from one to many particles when considering collectivity. Building on our recent work we want to study this challenging problem, starting from spin chains which presently receive much interest in theory and experiment. We also aim at first steps to extend our study to a broader class of interacting many-body systems.