arXiv 1109.39092011-09-18hep-th

全息临界点上的量子猝灭

Quantum Quench across a Holographic Critical Point

Pallab Basu, Sumit R. Das

备注：: 30 pages, 4 figures
DOI：: 10.1007/JHEP01(2012)103

摘要：

利用AdS/CFT方法研究了强耦合场论中临界点处的量子猝灭问题。该模型涉及一个探测中性标量场与质量平方$m^2$在范围$-9/4 < m^2 < -3/2$在一个$AdS_4$带电黑膜背景。对于给定的膜背景，存在一个临界质量平方$m_c^2$，使得对于$m^2 < m_c^2$，标量场凝聚。当$m^2 = m_c^2$和对偶算子的源为零时，该理论是临界的。在临界点处，体线性化问题的径向算子具有零模。我们研究了含时源$J(t)$或含零时体质量$m(u)$在临界点附近的序参量动力学。我们表明，在临界区域的动态最初缓慢的变化占主导地位的零模式：这导致了一个有效的描述的朗道-金斯伯格型动态与{ \em线性}时间导数。从有序相的绝热初始条件开始，我们发现有序参数在$t_\star$时刻降为零，该时刻晚于$(m_c^2-m^2)$或$J$达到零的时刻。在临界区域，$t_\star$，以及序参量偏离其绝热值，与变化率成比例，指数由静态临界行为确定。序参量的数值结果与这些预期是一致的。

英文摘要：

We study the problem of quantum quench across a critical point in a strongly coupled field theory using AdS/CFT techniques. The model involves a probe neutral scalar field with mass-squared $m^2$ in the range $-9/4 < m^2 < -3/2$ in a $AdS_4$ charged black brane background. For a given brane background there is a critical mass-squared, $m_c^2$ such that for $m^2 < m_c^2$ the scalar field condenses. The theory is critical when $m^2 = m_c^2$ and the source for the dual operator vanishes. At the critical point, the radial operator for the bulk linearized problem has a zero mode. We study the dynamics of the order parameter with a time dependent source $J(t)$, or a null-time dependent bulk mass $m(u)$ across the critical point. We show that in the critical region the dynamics for an initially slow variation is dominated by the zero mode : this leads to an effective description in terms of a Landau-Ginsburg type dynamics with a {\em linear} time derivative. Starting with an adiabatic initial condition in the ordered phase, we find that the order parameter drops to zero at a time $t_\star$ which is later than the time when $(m_c^2-m^2)$ or $J$ hits zero. In the critical region, $t_\star$, and the departure of the order parameter from its adiabatic value, scale with the rate of change, with exponents determined by static critical behavior. Numerical results for the order parameter are consistent with these expectations.

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英文摘要：

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