Related papers: Quantum bounds on the generalized Lyapunov exponents

Quantum bounds on the generalized Lyapunov exponents

URL: http://arxiv.org/abs/2212.10123v1
Date: Tue, 20 Dec 2022 09:46:32 GMT
Title: Quantum bounds on the generalized Lyapunov exponents
Authors: Silvia Pappalardi and Jorge Kurchan
Abstract summary: We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem. Our findings are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents $L_q$ via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger $q$ are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.

Related papers

Quantum work statistics across a critical point: full crossover from sudden quench to the adiabatic limit [17.407913371102048]
Adiabatic and sudden-quench limits have been studied in detail, but the quantum work statistics along the crossover connecting these limits has largely been an open question. Here we obtain exact scaling functions for the work statistics along the full crossover from adiabatic to sudden-quench limits for critical quantum impurity problems. These predictions can be tested in charge-multichannel Kondo quantum dot devices, where the dissipated work corresponds to the creation of nontrivial excitations.
arXiv Detail & Related papers (2025-02-03T18:36:07Z)
The Lyapunov exponent as a signature of dissipative many-body quantum chaos [0.0]
A positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. We show that a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos.
arXiv Detail & Related papers (2024-03-19T02:07:22Z)
Quantum dissipation and the virial theorem [22.1682776279474]
We study the celebrated virial theorem for dissipative systems, both classical and quantum. The non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.
arXiv Detail & Related papers (2023-02-23T13:28:11Z)
Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels [17.153903773911036]
We prove an entropic uncertainty relation for two quantum channels. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy.
arXiv Detail & Related papers (2023-01-20T02:34:31Z)
Krylov complexity in quantum field theory, and beyond [44.99833362998488]
We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
arXiv Detail & Related papers (2022-12-29T19:00:00Z)
An operator growth hypothesis for open quantum systems [0.0]
We study the dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model. We conjecture to be generic for any dissipative (open) quantum systems.
arXiv Detail & Related papers (2022-12-12T19:00:12Z)
Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
arXiv Detail & Related papers (2022-07-28T17:58:59Z)
Quantum chaos in a weakly-coupled field theory with nonlocality [0.7993126899701837]
We compute the Lyapunov exponent of exponential growth in the large Moyal-scale limit to leading order in the t'Hooft coupling and $1/N$. In this limit, the Lyapunov exponent remains comparable in magnitude to (and somewhat smaller than) the exponent in the commutative case.
arXiv Detail & Related papers (2021-11-21T20:32:57Z)
Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
arXiv Detail & Related papers (2021-11-01T16:35:41Z)
Extracting classical Lyapunov exponent from one-dimensional quantum mechanics [0.0]
A commutator $[x(t),p]$ in one-dimensional quantum mechanics exhibits remarkable properties. The Lyapunov exponent computed through the out-of-time-order correlator (OTOC) $langle [x(t),p]2 rangle $ precisely agrees with the classical one. We find two situations in which the OTOCs show exponential growth the classical Lyapunov exponent of the peak.
arXiv Detail & Related papers (2021-05-20T08:57:30Z)
Topological lower bound on quantum chaos by entanglement growth [0.7734726150561088]
We show that for one-dimensional quantum cellular automata there exists a lower bound on quantum chaos quantified by entanglement entropy. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians.
arXiv Detail & Related papers (2020-12-04T18:48:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.