来自非平衡路径积分的量子自由能差：II。谐振子的收敛性质
Quantum free energy differences from non-equilibrium path integrals: II. Convergence properties for the harmonic oscillator
摘要：
将计算量子自由能差的非平衡路径积分方法应用于均匀变化强度的简谐阱中的量子粒子，目的是建立正则化路径积分中自由度M趋于无穷大时功分布和自由能的收敛性质.工作分布收敛时，M趋于无穷大，无论开关速度，导致有限的结果时，Jarzynski非平衡工作关系或克鲁克斯波动关系的自由能差。收敛的性质取决于正则化方法。对于傅立叶方法，自由能差和功分布的收敛性为1/M，而当使用珠正则化过程时，这两个量都收敛于1/M^2。这些结果更一般的系统的影响进行了讨论。
英文摘要：
Non-equilibrium path integral methods for computing quantum free energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of the work distribution and free energy as the number of degrees of freedom M in the regularized path integrals goes to infinity. The work distribution is found to converge when M tends to infinity regardless of the switching speed, leading to finite results for the free energy difference when the Jarzynski non-equilibrium work relation or the Crooks fluctuation relation are used. The nature of the convergence depends on the regularization method. For the Fourier method, the convergence of the free energy difference and work distribution go as 1/M, while both quantities converge as 1/M^2 when the bead regularization procedure is used. The implications of these results to more general systems are discussed.
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