Corpus ID: 235731780

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

@inproceedings{Maier2021HolographicKE,
  title={Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum},
  author={Georg Maier and Andreas Schafer and Sebastian Waeber},
  year={2021}
}
In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the KolmogorovSinai entropy, is given by the sum over all positive Lyapunov exponents. A natural question is whether a similar relation is valid for quantum systems. We argue that the Maldacena-Shenker-Stanford bound on quantum Lyapunov exponents λ implies that the… Expand

Figures from this paper

References

SHOWING 1-10 OF 44 REFERENCES
Chaos and quantum thermalization.
  • Srednicki
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
TLDR
It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics. Expand
Many-body chaos and energy dynamics in holography
A bstractRecent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-pointExpand
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory andExpand
Thermalization and its mechanism for generic isolated quantum systems
TLDR
It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki. Expand
Kolmogorov-Sinai Entropy Rate versus Physical Entropy
We elucidate the connection between the Kolmogorov-Sinai entropy rate {kappa} and the time evolution of the physical or statistical entropy S . For a large family of chaotic conservative dynamicalExpand
Second law of quantum complexity
We give arguments for the existence of a thermodynamics of quantum complexity that includes a “second law of complexity.” To guide us, we derive a correspondence between the computational (circuit)Expand
Chaotic behavior in classical Yang-Mills dynamics
Institut fu¨r Theoretische Physik, Universita¨t Regensburg, D-93040 Regensburg, Germany(Dated: August 9, 2010)Understanding the underlying mechanisms causing rapid thermalization deduced forExpand
On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
A bstractPole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics andExpand
A bound on chaos
A bstractWe conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlationExpand
Thermalization of strongly coupled field theories.
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scaleExpand
...
1
2
3
4
5
...