用量子力学猎取鸭（Duck hunting with quantum mechanics）
Duck hunting with quantum mechanics
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中文总结 AI 辅助
该研究打通奇异摄动理论的经典与半经典分支，证明经典鸭解是量子瞬子的影子，以过阻尼约瑟夫森结为例分析并数值验证，确定鸭解窗口为相邻夏皮罗台阶间的指数窄间隙。
中文摘要 AI 辅助
我们打通了奇异摄动理论的两个分支：慢快系统的经典理论与量子力学系统的半经典方法。针对一类特定但具物理重要性的动力学系统，我们证明纯经典的奇异对象——所谓的鸭解（canard solutions），是对应量子系统中瞬子（instantons）的影子。我们表明鸭解存在于参数空间的某个区域，其边界由瞬子作用量决定。我们以过阻尼约瑟夫森结（overdamped Josephson junction）为例做了分析说明，并通过数值计算予以验证。对于约瑟夫森结，鸭解窗口是相邻夏皮罗台阶（Shapiro steps）之间指数级狭窄的间隙。
英文摘要
We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.
发表机构
- Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
- Moscow Institute of Physics and Technology（莫斯科物理技术学院）
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