Quantum chaos, integrability, and late times in the Krylov basis - INSPIRE

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Quantum chaos, integrability, and late times in the Krylov basis

Vijay Balasubramanian
(
- Pennsylvania U. and
- Santa Fe Inst. and
- Vrije U., Brussels
)
,
Javier M. Magan
(
- Balseiro Inst., San Carlos de Bariloche
)
,
Qingyue Wu
(
- Pennsylvania U.
)

Dec 6, 2023

18 pages

Published in:

Phys.Rev.E 111 (2025) 1, 014218

Published: Jan 15, 2025

e-Print:

2312.03848 [hep-th]

DOI:

10.1103/PhysRevE.111.014218 (publication)

View in:

ADS Abstract Service

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Abstract: (APS)

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by random matrix theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffice to produce the full long-time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long-time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Finally, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

matrix model: random
chaos
Lanczos
integrability
initial state
covariance
spectral
energy eigenstate
statistics
universality

References(53)

Figures(10)

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