Path integral approach to quantum thermalization

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Abstract
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 σ model of disordered systems, the G 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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Funding Information
  • Deutsche Forschungsgemeinschaft (2004/1 390534769)
  • National Research Foundation of Korea
  • Ministry of Education (RS-2025-00521598)
  • Ministry of Science and ICT, South Korea (2020R1A5A1016518)
  • CRC network TR 183 (277101999)

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