English

On Quantum Complexity

High Energy Physics - Theory 2023-08-15 v3 Statistical Mechanics Quantum Physics

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.

Keywords

Cite

@article{arxiv.2209.14689,
  title  = {On Quantum Complexity},
  author = {Mohsen Alishahiha},
  journal= {arXiv preprint arXiv:2209.14689},
  year   = {2023}
}

Comments

6 pages, V3: Published version + a comment on the saturation phase of complexity