Relaxation Dynamics after the Removal of a Static Force: Binary Operators and Impact of Eigenstate Thermalization

We study the relaxation dynamics of expectation values under unitary time evolution for a certain class of initial states. The latter are thermal states of the quantum system in the presence of an additional static force which, however, become nonequilibrium states when this force is eventually removed. While for weak forces the dynamics is well captured by linear response theory (LRT), the case of strong forces, i.e., initial states far away from equilibrium, is highly nontrivial.
Employing a combination of analytical arguments as well as numerical calculations for interacting quantum lattice models, we unveil that the nonequilibrium dynamics at high temperatures can, in various cases, be universally generated by a single correlation function in the entire regime close to and far away from equilibrium. Specifically, we consider so-called binary operators and study, as an example, the dynamics of spinless fermions in a random potential. In addition, we discuss the role of the eigenstate thermalization hypothesis (ETH) and establish a connection between ETH and LRT.

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