Abstract
Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.
Highlights
Because the GUE measure is invariant under unitary conjugation, we can equivalently evaluate this average over angles as an integral over the unitary group U(N ), i.e
We derive here an explicit form of the spectral form factor that provides an alternative form to the result in [27], with a corrected sign and expression
Starting with the definition of the connected form factor in (44), we expand the square value in Eq (8) and write
Summary
Work probability distribution function.— Let us consider a driven, isolated system described by the instantaneous Hamiltonian at time s. We shall use the average of an arbitrary operator Oover the probability density function ρ(H ) from which realizations of the chaotic Hamiltonian Hare sampled in GUE. This average can be written as [19, 23]. Knowledge of the density of states will allow us to characterize the work statistics in systems of arbitrary size To this end, we shall need the connected two-level correlation function [19], ρ(c2)(E, E ). This is of particular importance to describe the quantum work statistics of finite quantum chaotic systems as well as to explore the connections between work fluctuations and information scrambling
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