含噪声复Ginzburg-Landau方程的临界初始滑移标度
Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
摘要：
利用微扰场论重整化群方法研究了加性白噪声下复Ginzburg-Landau方程在连续非平衡相变附近的普适临界行为.这种随机偏微分描述了一个非常广泛的物理系统：耦合非线性振荡器受到外部噪声附近的霍普夫分岔不稳定性;自发结构形成的非平衡系统，例如，在周期性竞争的人口;和驱动耗散玻色-爱因斯坦凝聚，实现在开放系统的接口上的量子光学和多体物理，如冷原子气体和激子极化激元泵浦半导体量子阱中的光学腔。我们的出发点是一个嘈杂的，耗散的Gross-Pitaevski或非线性薛定谔方程，或等效的纯弛豫动力学起源于一个复值的朗道-金兹伯格功能，它推广了标准的平衡模型A临界动力学的非保守复杂的序参量字段。我们研究了这个系统在从高斯加权完全随机初始状态松弛的早期阶段的普遍临界行为。在这个关键的老化制度，时间平移不变性被打破，和动态的特点是由静态和动态的临界指数，以及一个独立的“初始滑移”指数。我们表明，一阶的上临界尺寸的尺寸展开，这个初始滑移指数在复杂的Ginzburg-Landau方程是相同的平衡模型A对应。此外，我们采用的重整化群流方程，以及构建一个合适的复杂的球形模型扩展认为，这一结论可能仍然适用于所有订单的微扰展开。
英文摘要：
We employ the perturbative field-theoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose--Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross-Pitaevski or non-linear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau-Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent `initial-slip' exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg-Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion.
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