Quantum chaos and the complexity of spread of states
- URL: http://arxiv.org/abs/2202.06957v2
- Date: Wed, 20 Apr 2022 16:47:36 GMT
- Title: Quantum chaos and the complexity of spread of states
- Authors: Vijay Balasubramanian, Pawel Caputa, Javier Magan and Qingyue Wu
- Abstract summary: 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.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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