SciPost logo

SciPost Submission Page

Beyond Fermi's golden rule with the statistical Jacobi approximation

by David M. Long, Dominik Hahn, Marin Bukov, Anushya Chandran

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): David Long
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-30
Date submitted: 2023-11-21 15:25
Submitted by: Long, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


Many problems in quantum dynamics can be cast as the decay of a single quantum state into a continuum. The time-dependent overlap with the initial state, called the fidelity, characterizes this decay. We derive an analytic expression for the fidelity after a quench to an ergodic Hamiltonian. The expression is valid for both weak and strong quenches, and timescales before finiteness of the Hilbert space limits the fidelity. It reproduces initial quadratic decay and asymptotic exponential decay with a rate which, for strong quenches, differs from Fermi's golden rule. The analysis relies on the statistical Jacobi approximation (SJA), which was originally applied in nearly localized systems, and which we here adapt to well-thermalizing systems. Our results demonstrate that the SJA is predictive in disparate regimes of quantum dynamics.

Published as SciPost Phys. 15, 251 (2023)

Author comments upon resubmission

This revised manuscript includes several clarifications and corrections which address the reports of the referees.

List of changes

- New comment in the introduction on the relationship between strong-disorder RG and the SJA.
- New paragraph in Sec. 2.2 on models which show slower than exponential relaxation.
- Extra column in Table 1 giving the interpretation of each approximation.
- Corrected error terms in Eqs. (53, 65).
- New comment on higher order corrections in the perturbation strength in Sec. 4.3.3.
- New footnote on the estimate of the cutoff time in Sec. 4.3.4.
- New section on higher order corrections in the inverse many-body bandwidth (Sec. 4.3.5).
- Corrected description of the numerics at the beginning of Sec. 5.
- New inset in Fig. 8 showing oscillatory behavior.
- The footnote in Sec. 5.1 has been brought into the main text, and the damped oscillatory term has been explicitly noted.
- New paragraph in the discussion on the numerical computation of the Jacobi autocorrelation function and possible future research.
- Clarified discussion of Dyson Brownian motion in the discussion.
- New appendix A.4 calculating the leading correction to Eq. (3) in the inverse many-body bandwidth.
- Minor changes in wording throughout, and additional references.

Reports on this Submission

Anonymous Report 1 on 2023-11-23 (Invited Report)


I find the authors' replies sufficient and now recommend publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Login to report or comment