标题： 绝热近似应用于虚时间薛定谔方程及其在模拟退火中的应用 显示英文标题

标题： Adiabatic approximation for the imaginary-time Schroedinger equation and its application to simulated annealing

摘要： 我们为虚时间薛定谔方程制定了绝热近似。 所得的绝热条件由两个不等式组成，其中一个与实时间薛定谔方程的传统绝热条件一致，但另一个则不然。 我们将此绝热近似应用于经典伊辛模型的Markovian动力学分析中，该模型可以表述为虚时间薛定谔方程，以获得在模拟退火的长退火时间内系统达到基态的概率渐近公式。 利用这一形式，我们修正了Somma、Batista和Ortiz关于模拟退火收敛条件的理论。 显示英文摘要

摘要： We formulate an adiabatic approximation for the imaginary-time Schroedinger equation. The obtained adiabatic condition consists of two inequalities, one of which coincides with the conventional adiabatic condition for the real-time Schroedinger equation, but the other does not. We apply this adiabatic approximation to the analysis of Markovian dynamics of the classical Ising model, which can be formulated as the imaginary-time Schr\"odinger equation, to obtain an asymptotic formula for the probability that the system reaches the ground state in the limit of a long annealing time in simulated annealing. Using this form, we amend the theory of Somma, Batista, and Ortiz for a convergence condition for simulated annealing.