Operator growth and spread complexity in open quantum systems
arxiv(2024)
Abstract
Commonly, the notion of "quantum chaos” refers to the fast scrambling of
information throughout complex quantum systems undergoing unitary evolution.
Motivated by the Krylov complexity and the operator growth hypothesis, we
demonstrate that the entropy of the population distribution for an operator in
time is a useful way to capture the complexity of the internal information
dynamics of a system when subject to an environment and is, in principle,
agnostic to the specific choice of operator basis. We demonstrate its
effectiveness for the Sachdev-Ye-Kitaev (SYK) model, examining the dynamics of
the system in both its Krylov basis and the basis of operator strings. We prove
that the former basis minimises spread complexity while the latter is an
eigenbasis for high dissipation. In both cases, we probe the long-time dynamics
of the model and the phenomenological effects of decoherence on the complexity
of the dynamics.
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