Consistent quantum treatments of non-convex kinetic energies

• URL: http://arxiv.org/abs/2507.21993v1
• Date: Tue, 29 Jul 2025 16:44:08 GMT
• Title: Consistent quantum treatments of non-convex kinetic energies
• Authors: C. Koliofoti, M. A. Javed, R. -P. Riwar,
• Abstract summary: We show that seemingly inconsistent descriptions of a Hamiltonian a classical Lagrangian can both be valid depending on the coupling.<n>We provide efficient methods to treat anomalous capacitors, non kinetic energies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Wilczek and Shapere's classical time crystal, or nonlinear capacitors) 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. Essentially there occurs a dissipative phase transition from a non-convex Hamiltonian to a convex Lagrangian regime, involving exceptional points in imaginary time. This resolves apparent inconsistencies and provide computationally efficient methods to treat anomalous, nonconvex kinetic energies.

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