Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics
| Autor: | Aron, Camille, Brunet, Éric, Mitra, Aditi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 108, L241106 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.108.L241106 |
| Popis: | Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity $v$ is bounded by the light cone velocity $v_{\rm lc }$ set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity $v_{\rm lc}$, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity $v$. In the diffusive regime, we establish the relation $v^2/\lambda_{\rm FKPP} \sim D_{\rm el}$ where $\lambda_{\rm FKPP}$ is the Lyapunov exponent set by the inelastic scattering rate and $D_{\rm el}$ is the elastic diffusion constant. Comment: $4+\epsilon$ pages plus 15 pages of Appendix. Minor modifications (published version) |
| Databáze: | arXiv |
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