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Condensed Matter > Statistical Mechanics

Title: Hydrodynamic Theory of the Connected Spectral Form Factor

Abstract: One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum. Prior to the inverse level spacing time, random matrix theory predicts a `ramp' of increasing variance in the connected part of the spectral form factor. However, in realistic quantum chaotic systems, the finite time dynamics of the spectral form factor is much richer, with the pure random matrix ramp appearing only at sufficiently late time. In this article, we present a hydrodynamic theory of the connected spectral form factor prior to the inverse level spacing time. We start from a discussion of exact symmetries and spectral stretching and folding. We then derive a general formula for the spectral form factor of a system with almost-conserved sectors in terms of return probabilities and spectral form factors within each sector. Next we argue that the theory of fluctuating hydrodynamics can be adapted from the usual Schwinger-Keldysh contour to the periodic time setting needed for the spectral form factor, and we show explicitly that the general formula is recovered in the case of energy diffusion. We also initiate a study of interaction effects in this modified hydrodynamic framework and show how the Thouless time, defined as the time required for the spectral form factor to approach the pure random matrix result, is controlled by the slow hydrodynamics modes.
Comments: v3: Removed didactic sections, added in section on Floquet dynamics
Subjects: Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
Cite as: arXiv:2012.01436 [cond-mat.stat-mech]
  (or arXiv:2012.01436v4 [cond-mat.stat-mech] for this version)

Submission history

From: Michael Winer [view email]
[v1] Wed, 2 Dec 2020 19:00:01 GMT (1409kb,D)
[v2] Sun, 6 Dec 2020 20:42:13 GMT (1411kb,D)
[v3] Tue, 31 Aug 2021 18:00:57 GMT (2424kb,D)
[v4] Fri, 11 Mar 2022 21:59:18 GMT (2522kb,D)

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