TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.042
TI  - Traveling discontinuity at the quantum butterfly front
PY  - 2023/08/02
UR  - https://www.scipost.org/SciPostPhys.15.2.042
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 042
A1  - Aron, Camille
AU  - Brunet, Éric
AU  - Mitra, Aditi
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.2.042,
	title={{Traveling discontinuity at the quantum butterfly front}},
	author={Camille Aron and Éric Brunet and Aditi Mitra},
	journal={SciPost Phys.},
	volume={15},
	pages={042},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.042},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.042},
}