经典Langmuir波系的BCS型二级相变
BCS-type second-order phase transition of classical Langmuir wave system
摘要：
从理论上和数值上证实了经典朗缪尔波系统的BCS型二级相变。跃迁发生在两种状态之间：朗缪尔波湍流（LWT）和朗缪尔波超连续谱（LWSC），当系统中激发一定数量的等离子体激元（等离子体波量子）时，后者表现出具有显著时空相干性的宽功率谱。在LWT-LWSC转变中，调制不稳定性和由此产生的等离子体激元对的产生是超导态中库珀不稳定性和库珀对产生的经典对应物。超导态下库珀对的玻色-爱因斯坦凝聚被LWSC中等离激元对的仓本凝聚-卷吸所取代。LWSC态的序参量（定义为等离子体激元对的平均场）具有显著的值，这清楚地表明宏观数量的等离子体激元对占据了LWSC中具有相同相位的单个动量态。时空相干性的出现和相位随机性的降低分别被认为是长程序和自发对称性破缺的发展，表明LWT-LWSC相变是一个二级相变现象.通过这种转变，LWT的U（1）对称性被打破。在等离子体物理方面，LWSC是以其无阻尼性质为特征的所谓Bernstein-Greene-Kruskal模式。
英文摘要：
The BCS-type second-order phase transition of a classical Langmuir wave system is identified theoretically and numerically. The transition takes place between two states: Langmuir wave turbulence (LWT) and Langmuir wave supercontinuum (LWSC), the latter of which exhibits broad power spectra with significant spatiotemporal coherence when a certain number of plasmons (plasma wave quanta) are excited in the system. In the LWT-LWSC transition, the modulational instability and resulting creation of plasmon pairs are the classical counterparts of the Cooper instability and creation of Cooper pairs in superconducting states. The Bose-Einstein condensation of Cooper pairs in superconducting states is replaced by the Kuramoto oscillator-entrainment of plasmon pairs in a LWSC. The order parameter of the LWSC state, which is defined as the mean field of the plasmon pairs, takes on a significant value, which clearly indicates that a macroscopic number of plasmon pairs occupy a single momentum state with an identical phase in the LWSC. The emergence of spatiotemporal coherence and the decrease in the phase randomization are considered as development of long-range order and spontaneous symmetry breaking, respectively, indicating that the LWT-LWSC transition is a second order phase transition phenomenon. By this transition, U(1) symmetry of LWT is broken. The LWSC is, in terms of plasma physics, a so-called Bernstein-Greene-Kruskal mode characterized by its undamped nature.
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