Special QLunch: Sarang Gopalakrishnan

Speaker: Sarang Gopalakrishnan, Princeton University

Title: Temporal correlation functions and Ruelle resonances in generic quantum dynamics

Abstract: I will discuss two results related to the decay of temporal correlation functions in generic quantum dynamics. First, I will address dynamics with no conservation laws. In this case, correlation functions decay exponentially; moreover, in the presence of noise, this exponential decay rate sets the gap of the quantum channel generating the dynamics. In the case with conservation laws, by contrast, I will argue that no local correlation function decays with an exponential

rate: even when (by symmetry) one can construct operators that are orthogonal to all hydrodynamic modes, the correlations of these operators decay subexponentially, due to rare-region effects.

ill discuss two results related to the decay of temporal correlation functions in generic quantum dynamics. First, I will address dynamics with no conservation laws. In this case, correlation functions decay exponentially; moreover, in the presence of noise, this exponential decay rate sets the gap of the quantum channel generating the dynamics. In the case with conservation laws, by contrast, I will argue that no local correlation function decays with an exponential

rate: even when (by symmetry) one can construct operators that are orthogonal to all hydrodynamic modes, the correlations of these operators decay subexponentially, due to rare-region effects.