Bounds on Chaos from the Eigenstate Thermalization Hypothesis

Murthy, Chaitanya; Srednicki, Mark

doi:10.1103/physrevlett.123.230606

Cited by 130 publications

(98 citation statements)

References 22 publications

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“…It is interesting to note that, as λ L is defined via a four-point correlation function (the OTOC), while α depends on a two-point correlation function (C(t)), the bound (37) can be interpreted as a relation between correlation functions of distinct nature. Such a relation is, to our knowledge, rather unusual (see [50] for a recent result). However, this point of view is not how we derived (37); an alternative proof working directly with the correlation functions would be illuminating.…”

Section: Growth Rate As a Bound On Chaosmentioning

confidence: 77%

A Universal Operator Growth Hypothesis

et al. 2019

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We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate α in generic systems, with an extra logarithmic correction in 1d. The rate α -an experimental observable -governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-N limits. Moreover, α upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents λL ≤ 2α, which complements and improves the known universal low-temperature bound λL ≤ 2πT . We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants. CONTENTS

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Section: Growth Rate As a Bound On Chaosmentioning

confidence: 77%

A Universal Operator Growth Hypothesis

et al. 2019

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“…Both the bounds on this rate and the Lyapunov exponent were shown to follow from the eigenstate thermalization hypothesis in Ref. [17]. (13) The circuit complexity was suggested to be related to the logarithm of the Loschmidt echo in Ref.…”

Section: A Spectral Form Factormentioning

confidence: 99%

Conformal field theory and the web of quantum chaos diagnostics

Kudler-Flam

Nie

Ryu

2020

J. High Energ. Phys.

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We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from "large-N" limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.

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“…Definida c o mo [A(0), B(t)], essa quantidade mede a influência d e u m a perturbação causada pelo operador A, sobre uma medida posterior do operador B, e sua dependência temporal é sens´ıvel à dinâmica clássica [14]. Aliás, os dois problemas parecem estar relacionados [15].…”

Section: Sistemas Caóticosunclassified

O Gato e a Borboleta: propriedades quânticas de sistemas caóticos

Novaes

2021

Rev. Bras. Ensino Fís.

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Neste artigo apresento uma introdução ao problema do caos quântico, ou seja, da caracterização e do tratamento de sistemas quânticos cujo análogo clássico tem dinâmica caótica. Duas das principais abordagens a esse problema são discutidas: uma delas é estatística, fazendo uso de matrizes aleatórias, enquanto a outra é baseada na aproximação semiclássica. Resultados obtidos por meio dessas abordagens são mencionados para sistemas fechados (funções de correlação espectral), para transporte (momentos como condutância e ruído de disparo) e para ressonâncias (lei de Weyl fractal e funções de onda fractais).

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Bounds on Chaos from the Eigenstate Thermalization Hypothesis

Cited by 130 publications

References 22 publications

A Universal Operator Growth Hypothesis

A Universal Operator Growth Hypothesis

Conformal field theory and the web of quantum chaos diagnostics

O Gato e a Borboleta: propriedades quânticas de sistemas caóticos

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