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We investigate how the observable relaxation behavior of an isolated quantummany-body system is modified in response to weak-to-moderate perturbationswithin a nonperturbative typicality framework. A key role is played by theso-called perturbation profile, which characterizes the dependence of theperturbation matrix elements in the eigenbasis of the unperturbed Hamiltonianon the difference of the corresponding energy eigenvalues. In particular, abanded matrix structure is quantitatively captured by a perturbation profilewhich approaches zero for large energy differences. The temporal modificationof the relaxation is linked to the perturbation profile via a nonlinearintegral equation, which admits approximate analytical solutions forsufficiently weak and strong perturbations, and for which we work out anumerical solution scheme in the general case. As an example, we consider aspin lattice model with a pronounced banded matrix structure, and we find verygood agreement of the numerics with our analytical predictions without any freefit parameter.

Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure