Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel pith:DDETVV5Lrecord.jsonopen to challenge →
read the original abstract
In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. In this article we develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all $q$-body interactions. We derive the full operator growth structure in the large $q$ limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.
This paper has not been read by Pith yet.
Forward citations
Cited by 6 Pith papers
-
Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
-
Thermal two-point functions in SYK and complex-time singularities
The large-N SYK thermal two-point function exhibits complex-time singularities—an effective-temperature pole and a subleading bouncing-geodesic-like singularity—that persist from infinite to zero temperature.
-
Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity ...
-
Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island
In the double-scaled SYK model with an end-of-the-world brane, the boundary algebra for a single-sided black hole is a type II1 von Neumann factor with non-trivial commutant, preventing full bulk reconstruction and cr...
-
Toward Krylov-based holography in double-scaled SYK
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-ge...
-
Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-inte...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.