Global Symmetry and Maximal Chaos

Abstract

In this note we study chaos in generic quantum systems with a global symmetry generalizing seminal work [arXiv : 1503.01409] by Maldacena, Shenker and Stanford. We conjecture a bound on instantaneous chaos exponent in a thermodynamic ensemble at temperature $T$ and chemical potential $\mu$ for the continuous global symmetry under consideration. For local operators which could create excitation up to some fixed charge, the bound on chaos (Lyapunov) exponent is independent of chemical potential ${\lambda }_L\le \frac{2\pi T}{\hslash }$. On the other hand when the operators could create excitation of arbitrary high charge, we find that exponent must satisfy ${\lambda }_L\le \frac{2\pi T}{(1-|\frac{\mu }{{\mu }_c}|)\hslash }$, where ${\mu }_c$ is the maximum value of chemical potential for which the thermodynamic ensemble makes sense. As specific examples of quantum mechanical systems we consider conformal field theories. In a generic conformal field theory with internal $U(1)$ symmetry living on a cylinder the former bound is applicable, whereas in more interesting examples of holographic two dimensional conformal field theories dual to Einstein gravity, we argue that later bound is saturated in presence of a non-zero chemical potential for rotation.

25 pages

References in corpus (28)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Black holes as mirrors: quantum information in random subsystems
• Chaos in quantum channels
• Localized shocks
• Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes
• Multiple Shocks
• Two-dimensional conformal field theory and the butterfly effect
• Many-body chaos at weak coupling
• A quantum hydrodynamical description for scrambling and many-body chaos
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• Semiclassics, Goldstone Bosons and CFT data
• Onset of many-body chaos in the $O(N)$ model
• Bounds on chaos from the eigenstate thermalization hypothesis
• Models of AdS_2 Backreaction and Holography
• Conformal Bootstrap, Universality and Gravitational Scattering
• $T\overline{T}$ in AdS${}_2$ and Quantum Mechanics
• Notes on Melonic $O(N{)}^{q-1}$ Tensor Models
• Conformal Bootstrap At Large Charge
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• Chaos in the black hole S-matrix
• Scrambling without chaos in RCFT
• Chaos in the butterfly cone
• A Critique of the Fuzzball Program
• Soft mode and interior operator in Hayden-Preskill thought experiment
• Thermalization and chaos in QED${}_3$

Cited by in corpus (3)

• Chaos in the butterfly cone
• Phase transition and chaos in charged SYK model
• Rotating Black Holes in AdS, Extremality and Chaos