Department of Physics, National University of Singapore, Singapore 117546.
NUS Graduate School for Integrative Science and Engineering, Singapore 117597.
Phys Rev E. 2017 Oct;96(4-1):042119. doi: 10.1103/PhysRevE.96.042119. Epub 2017 Oct 9.
A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change ΔF of a system at inverse temperature β from an ensemble average of nonequilibrium exponential work, i.e., 〈e^{-βW}〉=e^{-βΔF}. The number of experimental work values needed to reach a given accuracy of ΔF is determined by the variance of e^{-βW}, denoted var(e^{-βW}). We discover in this work that var(e^{-βW}) in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging var(e^{-βW}) at sufficiently low temperatures, markedly different from the classical behavior. The divergence of var(e^{-βW}) indicates the too-far-from-equilibrium nature of a nonadiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test the Jarzynski equality.
一个具有重要理论和实验意义的结果是，雅可比等式（Jarzynski equality）预测了在逆温度β下系统的自由能变化ΔF，可以通过非平衡指数功的系综平均值来得到，即〈e^{-βW}〉=e^{-βΔF}。达到给定的ΔF 精度所需的实验功值的数量取决于 e^{-βW}的方差，记为 var(e^{-βW})。我们在这项工作中发现，在谐波和非谐波哈密顿系统中，var(e^{-βW})在非绝热功协议中会系统地发散，即使绝热协议不会遭受这种发散。这种发散可以看作是功涨落中的一种动态诱导相变。以具有时变俘获频率的量子谐振子为例，任何非绝热功协议在足够低的温度下都会产生发散的 var(e^{-βW})，这与经典行为明显不同。var(e^{-βW})的发散表明非绝热功协议的离平衡性质，因此有必要应用设计的控制场来抑制量子功涨落，以检验雅可比等式。
