磁环境中的全息布朗运动
Holographic Brownian Motion in Magnetic Environments
摘要：
利用规范/引力对应，我们研究了有限温度下两个强耦合系统中重夸克的动力学：有磁场存在的Super-Yang-Mills系统和非对易Super-Yang-Mills系统.在前者中，我们的结果与弱耦合理论的预期行为定性一致。在后者中，我们提出了一个朗之万方程，占非交换性的影响，我们发现新的有趣的功能。该方程类似于存在磁场时的布朗运动的结构，并意味着沿非对易方向的涨落是相关的。此外，我们的结果表明，粘性小于交换的情况下，夸克的扩散性质不受非交换性。最后，我们计算了随机力自相关器，并验证了涨落耗散定理在非交换性存在的情况下成立。
英文摘要：
Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in two strongly-coupled systems at finite temperature: Super-Yang-Mills in the presence of a magnetic field and non-commutative Super-Yang-Mills. In the former, our results agree qualitatively with the expected behavior from weakly-coupled theories. In the latter, we propose a Langevin equation that accounts for the effects of non-commutativity and we find new interesting features. The equation resembles the structure of Brownian motion in the presence of a magnetic field and implies that the fluctuations along non-commutative directions are correlated. Moreover, our results show that the viscosity is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.
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