PIRSA:18110101

Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK

Streicher, A. (2018). Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK. Perimeter Institute. https://pirsa.org/18110101

Streicher, Alexandre. Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK. Perimeter Institute, Nov. 26, 2018, https://pirsa.org/18110101 

          @misc{ pirsa_PIRSA:18110101,
            doi = {10.48660/18110101},
            url = {https://pirsa.org/18110101},
            author = {Streicher, Alexandre},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {nov},
            note = {PIRSA:18110101 see, \url{https://pirsa.org}}
          }

Alexandre Streicher

DOI 10.48660/18110101
Collection
Talk Type Scientific Series
Subject

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. 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.