论文标题
对于开放和孤立的量子系统的几何方法预测的失败预测过多工作缩放
Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
论文作者
论文摘要
寻找最佳协议的任务，以最大程度地减少长期但有限持续时间$τ$的热力学过程的能量成本。我们通过封闭的汉密尔顿量子系统的绝热扰动理论以一种严格而系统的方式来解决这个问题。我们的主要发现是$ 1/τ^2 $缩放大型$τ$在Gapped Systems中的多余工作。该结果与几何方法的$ 1/τ$预测相反，这是基于靠近规范平衡的开放系统的缓慢演变。相反，我们的方法不会导致明显的几何解释。此外，由于热力学工作不取决于如何将孤立的量子系统分为感兴趣的系统及其环境，因此我们的结果意味着即使对于开放系统，几何方法预测的失败也是如此。此外，我们提供了替代优化程序，既适用于通过绝热扰动理论描述的缓慢变化的过程以及线性响应理论描述的弱变化过程。我们的发现是基准测试的，并通过应用于驱动的横向场链的应用确认。
The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $τ$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the adiabatic perturbation theory of closed Hamiltonian quantum systems. Our main finding is a $1/τ^2$ scaling of the excess work for large $τ$ in gapped systems. This result is at odds with the $1/τ$ prediction of the geometric approach to optimization, which is predicated on the slow evolution of open systems close to canonical equilibrium. In contrast, our approach does not lead to an obvious geometric interpretation. Furthermore, as the thermodynamic work does not depend on how an isolated quantum system is split into a system of interest and its environment, our results imply the failure of the geometric approach prediction even for open systems. Additionally, we provide alternative optimization procedures, both for slowly-varying processes described by adiabatic perturbation theory and for weakly-varying processes described by linear response theory. Our findings are benchmarked and confirmed through the application to the driven transverse-field Ising chain.
