Quantum chaos and the complexity of spread of states
By Vijay Balasubramanian, Paweł Caputa, Javier M. Magán, Qingyue Wu. Physical Review D, 2022
234 citations recorded by the source corpus.
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the"survival amplitude"for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear"ramp"up to a"peak"that is exponential in the entropy, followed by a"slope"down to a"plateau". These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a212c82d20fdd71ba82e3592f779f13c8b02e561
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Citations in the corpus
- Krylov complexity from integrability to chaos (2022, methodology): “In addition to the behavior of K-complexity for given individual quantum systems, such as the SYK model [3, 5, 6], 2D CFTs [18, 19], and more general symmetry-based Hamiltonian systems [20, 21], it is interesting and important to categorize the possible Krylov phenomenologies according to more unive”