论文标题
量子系统和随机性的时间演变
Time evolution in quantum systems and stochastics
论文作者
论文摘要
通过路径积分公式研究了非自动伴随二阶差异操作员的时间演变问题。通过使用某些潜在的随机微分方程来对路径积分进行显式计算，这些方程在计算路径积分时自然会出现，无论差分运算符的形式如何，都会导致相关度量的通用表达。然后考虑离散的非线性层次结构（DNL），并原则上提取了可求解的相应层次结构。层次结构的第一对成员对应于离散的随机运输和热方程。离散的随机汉堡方程也是通过Cole-HOPF转换的类似物获得的。还讨论了连续限制。
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential equations, which naturally emerge when computing the path integral, leads to a universal expression for the associated measure regardless of the form of the differential operators. The discrete non-linear hierarchy (DNLS) is then considered and the corresponding hierarchy of solvable, in principle, SDEs is extracted. The first couple members of the hierarchy correspond to the discrete stochastic transport and heat equations. The discrete stochastic Burgers equation is also obtained through the analogue of the Cole-Hopf transformation. The continuum limit is also discussed.
