Hamiltonian dynamics of a sum of interacting random matrices
ORAL
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, H=A+B.
We analytically obtain the late-time value of〈A(t)A(0)〉; this quantifies the non-relaxing part of the observable A.
The relaxation to this value is governed by a power-law determined by the spectrum of the Hamiltonian H, independent of the observable A.
For Gaussian matrices, we further compute out-of-time-ordered-correlators (OTOCs) and find that the existence of a non-relaxing part of A leads to modifications of the late time values and exponents.
Our results follow from exact resummation of a diagrammatic expansion and hyperoperator techniques.
We compute exact dynamical correlators governed by a Hamiltonian composed of two large interacting random matrices, H=A+B.
We analytically obtain the late-time value of〈A(t)A(0)〉; this quantifies the non-relaxing part of the observable A.
The relaxation to this value is governed by a power-law determined by the spectrum of the Hamiltonian H, independent of the observable A.
For Gaussian matrices, we further compute out-of-time-ordered-correlators (OTOCs) and find that the existence of a non-relaxing part of A leads to modifications of the late time values and exponents.
Our results follow from exact resummation of a diagrammatic expansion and hyperoperator techniques.
*The authors acknowledge support from the NSF through grant PHY-1752727.
This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, and at the Galileo Galilei Institute in Florence.
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Presenters
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Matteo Bellitti
- Boston Univ