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Quantum Dynamics in many-body systems is nowadays well understood via the Eigenstate Thermalization Hypothesis (ETH). According to ETH, local observables in the energy eigenbasis are pseudorandom matrices, whose statistical properties are smooth thermodynamic functions. In this talk, I will show how the full version of ETH, which encompasses correlations among matrix elements, can be rationalized theoretically using the language of Free Probability. The latter is a generalization of probability theory to non-commuting variables, with applications in combinatorics and random matrix theory. The mathematical structure of Free Probability also allows us to provide a link between quantum dynamics and k-designs, an important concept with applications in quantum information theory.

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Silvia Pappalardi, ITP Cologne
SR 1, Mathematical Institute, Weyertal 86-90
Contact: Joachim Krug