Relaxation of non-integrable systems and correlation functions
- URL: http://arxiv.org/abs/2112.09475v2
- Date: Mon, 10 Jan 2022 10:33:01 GMT
- Title: Relaxation of non-integrable systems and correlation functions
- Authors: Jonathon Riddell, Luis Pedro Garc\'ia-Pintos, \'Alvaro M. Alhambra
- Abstract summary: We investigate early-time equilibration rates of observables in closed many-body quantum systems.
We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical.
Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate early-time equilibration rates of observables in closed
many-body quantum systems and compare them to those of two correlation
functions, first introduced by Kubo and Srednicki. We explore whether these
different rates coincide at a universal value that sets the timescales of
processes at a finite energy density. We find evidence for this coincidence
when the initial conditions are sufficiently generic, or typical. We quantify
this with the effective dimension of the state and with a state-observable
effective dimension, which estimate the number of energy levels that
participate in the dynamics. Our findings are confirmed by proving that these
different timescales coincide for dynamics generated by Haar-random
Hamiltonians. This also allows to quantitatively understand the scope of
previous theoretical results on equilibration timescales and on random matrix
formalisms. We approach this problem with exact, full spectrum diagonalization.
The numerics are carried out in a non-integrable Heisenberg-like Hamiltonian,
and the dynamics are investigated for several pairs of observables and states.
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