场的准种演化与随机量子化的比较
A comparison between the quasi-species evolution and stochastic quantization of fields
摘要：
准物种方程描述了种群中随机个体携带给定基因组的概率的演化。在这里，我们映射的准物种方程的个人的自我繁殖人口的标量场的基本单位进行创建和湮灭过程的系综。在该映射中，群体的个体被映射到字段单元，并且其基因组被映射到字段值。选择性压力映射到系统的逆温度β，调节场的演化动力学。我们表明，准种方程，如果适用于一个合奏的场单元在小β极限，可以把现有的随机量子化方法。由准种方程描述的场单元的系综松弛到基本状态，描述了本质上耗散的动力学。对于二次色散关系，系统的平均能量<U>作为温度β的倒数的函数而变化。对于小的β值，平均能量<U>采用相对论形式，对于大的β值，平均能量<U>采用经典形式。
英文摘要：
The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of scalar field elementary units undergoing a creation and annihilation process. In this mapping, the individuals of the population are mapped to field units and their genome to the field value. The selective pressure is mapped to an inverse temperature βof the system regulating the evolutionary dynamics of the fields. We show that the quasi-species equation if applied to an ensemble of field units gives in the small βlimit can be put in relation with existing stochastic quantization approaches. The ensemble of field units described by the quasi-species equation relaxes to the fundamental state, describing an intrinsically dissipative dynamics. For a quadratic dispersion relation the mean energy <U> of the system changes as a function of the inverse temperature β. For small values of βthe average energy <U> takes a relativistic form, for large values of β, the average energy <U> takes a classical form.
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