DNA呼吸的动力学：弱噪声分析，有限时间奇异性和映射到量子库仑问题
Dynamics of DNA-breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem
摘要：
本文在Poland-Scheraga模型的基础上研究了双链DNA中变性泡的动力学。我们表明，长时间分布的DNA气泡的生存和大小的自相关函数可以从一个渐进的弱噪声的方法。特别是，低于熔化温度的气泡闭合对应于一个嘈杂的有限时间奇点。我们证明了相应的Fokker-Planck方程等价于一个量子库仑问题。低于熔化温度的气泡寿命与连续的散射状态的排斥库仑势;在熔化温度下的库仑势消失和底层的第一出口动力学表现出长时间的幂律尾;熔化温度以上，对应于一个有吸引力的库仑势，长时间的动力学控制的最低束缚态。相关性和有限尺寸效应进行了讨论。
英文摘要：
We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.
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