量子系统的时间演化与随机
Time evolution in quantum systems and stochastics
摘要：
利用路径积分方法研究了非自伴二阶微分算子的时间演化问题。显式计算的路径积分通过使用某些潜在的随机微分方程，这自然出现时计算的路径积分，导致一个通用的表达式相关联的措施，无论形式的微分算子。然后考虑离散非线性层次（DNLS），并提取相应的可解层次，原则上，SDES。该层次的第一对成员对应于离散的随机输运方程和热方程。通过模拟Cole-Hopf变换，得到了离散的随机Burgers方程。讨论了连续极限。
英文摘要：
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.
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