标题： 非凸动能的量子一致处理 显示英文标题

标题： Consistent quantum treatments of non-convex kinetic energies

摘要： 寻找量子哈密顿量与经典拉格朗日量之间一致关系的任务对于基本但普遍的技术如正则量子化和路径积分至关重要。 非凸动能（例如出现在非线性电容器或经典时间晶体中）提出了一个根本性问题：勒让德变换是不明确的，而更一般的勒让德-芬切尔变换通过定义消除了非凸性。 我们认为这种异常理论来自于良好定义的谐波理论的适当低能近似，我们证明了看似不一致的哈密顿量和拉格朗日描述都可以有效，这取决于与耗散环境的耦合强度。 在虚时间中涉及特殊点的情况下，会发生从非凸哈密顿量到凸拉格朗日区的耗散相变。 因此，我们的方法解决了明显的不一致性，并提供了计算上高效的方法来处理异常的、非凸动能。 显示英文摘要

摘要： The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies (which appear, e.g., in nonlinear capacitors or classical time crystals) pose a fundamental problem: the Legendre transformation is ill-defined, and the more general Legendre-Fenchel transformation removes nonconvexity essentially by definition. Arguing that such anomalous theories follow from suitable low-energy approximations of well-defined, harmonic theories, we show that seemingly inconsistent Hamiltonian and Lagrangian descriptions can both be valid, depending on the coupling strength to a dissipative environment. There occurs a dissipative phase transition from a nonconvex Hamiltonian to a convex Lagrangian regime, involving exceptional points in imaginary time. Our approach thus resolves apparent inconsistencies and provides computationally efficient methods to treat anomalous, nonconvex kinetic energies.