Global Symmetry and Maximal Chaos

Understand

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 \leq \frac{2 \pi T}{ \hbar} $.
• On the other hand when the operators could create excitation of arbitrary high charge, we find that exponent must satisfy $\lambda_L \leq \frac{2 \pi T}{(1-|\frac{\mu}{\mu_c}|) \hbar} $, where $\mu_c$ is the maximum value of chemical potential for which the thermodynamic ensemble makes sense.