哈密顿和薛定谔动力学的最优协议
Optimal protocols for Hamiltonian and Schrödinger dynamics
摘要：
对于外部可控的时变势系统，最优协议使给定控制参数的初始值和最终值之间的有限时间过渡中所花费的平均功最小化。对于初始热化系综，我们考虑经典系统的哈密顿演化和量子系统的薛定谔演化。在这两种情况下，我们表明，谐波势，最佳的工作是由绝热工作，即使在短的过渡时间的限制。这个结果是违反直觉的，因为绝热功比瞬时跳跃的功小得多。我们还进行了数值计算的最佳协议的哈密顿动力学的非谐四次潜力。对于一个两能级自旋系统，我们给出的例子中，绝热工作可以达到在有限或任意短的过渡时间取决于允许的参数空间。
英文摘要：
For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations of the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.
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