arXiv 1908.052812019-08hep-thcond-mat.quant-gascond-mat.stat-mechcond-mat.str-elmath-phmath.MP

全局对称性与极大混沌

Global Symmetry and Maximal Chaos

Indranil Halder

备注：: 25 pages

摘要：

在本文中，我们研究了具有全局对称性的一般量子系统中的混沌，推广了Maldacena，Shenker和Stanford的开创性工作[arXiv：1503.01409]。在连续的整体对称性下，我们推测了热力学系综在温度$T$和化学势$μ$下的瞬时混沌指数的一个界.对于能激发到某一固定电荷的局域算子，混沌的界（李雅普诺夫）指数与化学势$λ_L \leq \frac{2 πT}{ \hbar} $无关。另一方面，当算符能激发任意高电荷时，我们发现指数必须满足$λ_L \leq \frac{2 πT}{(1-|\fracμ{μ_c}|) \hbar} $，其中$μ_c$是热力学系综所能解释的化学势的最大值.作为量子力学系统的具体例子，我们考虑共形场论。在一个通用的共形场论与内部$U(1)$对称性生活在一个圆柱体上的前界是适用的，而在更有趣的例子全息二维共形场论双爱因斯坦引力，我们认为，后界是饱和存在的非零化学势旋转。

英文摘要：

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 $μ$ 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 $λ_L \leq \frac{2 πT}{ \hbar} $. On the other hand when the operators could create excitation of arbitrary high charge, we find that exponent must satisfy $λ_L \leq \frac{2 πT}{(1-|\fracμ{μ_c}|) \hbar} $, where $μ_c$ 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.

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