On Quantum Complexity
arXiv:2209.14689 · doi:10.1016/j.physletb.2023.137979
Abstract
The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibit linear growth at late times. The condition is to do with a possible pole structure the corresponding matrix elements may have. Based on the general expectation of complexity one may want to think of this quantity as a possible candidate for the quantum complexity. We note, however, that for the explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.
6 pages, V3: Published version + a comment on the saturation phase of complexity
References in corpus (2)
Cited by in corpus (8)
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- Fixing detailed balance in ancilla-based dissipative state engineering
- Krylov Complexity as a Probe for Chaos
- Position dependence of Nielsen complexity for the Thermofield double state
- Universal Time Evolution of Holographic and Quantum Complexity