Hydrodynamic Theory of the Connected Spectral form Factor

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 “ramp” increasing variance in connected part spectral form factor. However, realistic chaotic systems, finite-time dynamics factor much richer, with pure ramp appearing only at sufficiently late time. In this article, we present hydrodynamic prior We first derive general formula for system almost-conserved sectors terms return probabilities and factors within each sector. Next argue that fluctuating hydrodynamics can be adapted from usual Schwinger-Keldysh contour periodic time setting needed factor, show explicitly recovered case diffusion. also initiate study interaction effects modified framework how Thouless defined as required approach result controlled by slow modes. then extend formalism Floquet where expected but different coefficient, crossover Hamiltonian when drive weak. Taken together, these results establish an effective field correlations which computes corrections it earlier times.6 MoreReceived 15 December 2020Revised 12 January 2022Accepted 10 February 2022DOI:https://doi.org/10.1103/PhysRevX.12.021009Published American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article’s title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum chaosPhysical Systems1-dimensional spin chainsTechniquesRandom theorySachdev-Ye-Kitaev modelU(N) symmetryCondensed Matter, Materials & Applied PhysicsNonlinear DynamicsFluid Dynamics