Nonperturbative Resummation of Divergent Time-Local Generators

TL;DR

This paper develops a nonperturbative method to reconstruct and analyze the dynamics of open quantum systems from divergent time-local generators, revealing signatures of environmental effects and singularities.

Contribution

It introduces an analytic continuation approach to nonperturbatively resum divergent generators, enabling the reconstruction of reduced dynamics and diagnosis of noninvertibility in open quantum systems.

Findings

Explicit dynamical map for the spin-boson model that resums the TCL generator.

Identification of early-time anisotropy and phase shifts as signatures of environmental correlations.

Demonstration of a late-time singularity where the reduced dynamics becomes noninvertible.

Abstract

Time-local generators of open quantum systems are generically divergent at long times, even though the reduced dynamics remains regular. We construct, by analytic continuation, nonperturbative dynamical maps consistent with these generators. For the weak-coupling unbiased spin--boson model, this construction yields an explicit dynamical map that nonperturbatively resums the TCL generator and exposes how the divergences signal the approach to a singular time at which the reduced dynamics becomes noninvertible. The reconstructed map is validated against TEMPO simulations at short times and the exactly solvable rotating-wave model at all times. In the full spin--boson model, the same continuum mechanism produces both an early-time anisotropy, with a measurable phase shift that provides a signature of the environmental correlation and the pointer direction, and a late-time singularity at which the reduced dynamics becomes noninvertible. By contrast, in the rotating-wave model the map approaches this point without reaching it and remains invertible at all times. These results establish a nonperturbative framework for reconstructing reduced dynamics from divergent time-local generators, diagnosing the onset of noninvertibility, and identifying experimentally accessible early-time signatures of environment-induced anisotropy.