Path integral approach to quantum thermalization

초록

We introduce a quasiclassical Green's function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the nonlinear model of disordered systems, the ⁡Σ formalism for strong correlations, and real-time path integration, the theory is capable of describing a wide range of system classes and disorder models. It extends previous work beyond perturbation theory (in inverse Hilbert-space dimensions), enabling a description of thermalization dynamics from short scattering times, through the onset of ergodicity at an effective “Thouless time,” up to the many-body Heisenberg time. We illustrate the approach with two case studies: (1) a brickwork model of unitarily coupled quantum circuits with and without conserved symmetries and (2) an array of capacitively coupled quantum dots. Using the spectral form factor as a test observable, we find good agreement with numerical simulations. We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems in regimes of strong entanglement.

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