矩阵模型中的量子猝灭：动态相变、选择平衡和广义吉布斯熵
Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
摘要：
在一维单迹势幺正矩阵模型中考虑量子猝灭动力学。这个模型是可积的，并且已经在非临界弦论的背景下被研究过。我们发现动态相变，并研究量子临界点的作用。在时间演化过程中，我们发现了某一类观测量选择平衡的证据。平衡由广义吉布斯系综（GGE）控制，与标准吉布斯系综不同。我们计算的熵的生产，这是O（N）的大N矩阵。平衡的一个重要特征是能量级联的出现，让人想起湍流中的Richardson级联，在那里我们发现从初始长波长模式到逐渐变短的波长激发的能量流。我们讨论了平衡态和广义相对论在弦论和高自旋理论中的可能意义。在另一个相关的研究中，我们计算了时间演化的双迹酉矩阵模型，这是一个有效的理论，在IIA弦论中的D2膜的限制阶段。我们在这个矩阵模型中发现了类似的平衡和动力学转变。动力学跃迁与弦论中的格雷戈里-拉弗拉姆跃迁有关，并且可能与裸奇点的出现有关。
英文摘要：
Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unitary matrix model, which arises as an effective theory of D2 branes in IIA string theory in the confinement phase. We find similar equilibrations and dynamical transitions in this matrix model. The dynamical transitions are related to Gregory-Laflamme transitions in string theory and are potentially connected with the issue of appearance of naked singularities.
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