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Traveling discontinuity at the quantum butterfly front
by Camille Aron, Eric Brunet, Aditi Mitra
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
scipost_202301_00017v2
(pdf)
|
| Date accepted: |
2023-05-31 |
| Date submitted: |
2023-05-08 17:17 |
| Submitted by: |
Aron, Camille |
| Submitted to: |
SciPost Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- Condensed Matter Physics - Theory
- Quantum Physics
- Statistical and Soft Matter Physics
|
| Approach: |
Theoretical |
Abstract
We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.
