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arXiv · 2209.14689

On Quantum Complexity

Mohsen Alishahiha
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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.

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Mohsen Alishahiha. 2022-09-29. On Quantum Complexity. https://doi.org/10.1016/j.physletb.2023.137979

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