Hamiltonian Dynamics of a Sum of Interacting Random Matrices
arXiv:1908.02263 · doi:10.1103/PhysRevB.100.184201
Abstract
In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical correlators governed by a Hamiltonian composed of two large interacting random matrices, . We analytically obtain the late-time value of ; this quantifies the non-relaxing part of the observable . The relaxation to this value is governed by a power-law determined by the spectrum of the Hamiltonian , independent of the observable . For Gaussian matrices, we further compute out-of-time-ordered-correlators (OTOCs) and find that the existence of a non-relaxing part of leads to modifications of the late time values and exponents. Our results follow from exact resummation of a diagrammatic expansion and hyperoperator techniques.
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