Operator dynamics in Brownian quantum circuit
ORAL
Abstract
We view the operator spreading in chaotic evolution as a stochastic process of height growth. The height of an operator represents its spatial extent and a master equation governs the transition to higher operators. We derive and solve a master equation in a random N -spin model with all 2-body interactions. The mean height, being proportional to the squared commutator, will grow exponentially within log N scrambling time and saturates in a manner of logistic function. We propose that the chaos bound at finite temperature could be due to initial height biased towards the high operators, which has smaller Lyapunov exponent.
*XS and TZ are supported by a postdoctoral fellowship from the Gordon and Betty Moore Foundation, under the EPiQS initiative, Grant GBMF4304, at the Kavli Institute for Theoretical Physics. We acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1720256).
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Presenters
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Tianci Zhou
- University of California, Santa Barbara
- Kavli institute of theoretical physics