Quantum bounds and fluctuation-dissipation relations
In recent years, there has been intense attention on the constraints imposed by quantum mechanics on the dynamics of many-body systems at low temperatures, triggered by the postulation and derivation of quantum bounds on transport coefficients or on the chaos rate. In this talk I will discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is in fact a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, we describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.
S. Pappalardi, L. Foini, J. Kurchan, arXiv:2110.03497
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