The families of Hamiltonians sharing common symmetry structure

2023/03/23 by Cezary Gonera, Gonera, Cezary, Joanna Gonera +5
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #Protein Structure and Dynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2303.13165

openalex publication_date 2023/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a general procedure which allows to construct, starting from a given Hamiltonian, the whole family of new ones sharing the same set of unparameterized trajectories in phase space. The symmetry structure of this family can be completely characterized provided the symmetries of initial Hamiltonian are known. Our approach covers numerous models considered in literature as well as it allows to construct novel ones.. It provides a far reaching generalization of Hietarinta et al. coupling-constant metamorphosis method and another proof of Darboux theorem.

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