Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems

• URL: http://arxiv.org/abs/2208.09244v3
• Date: Sat, 27 Aug 2022 13:17:07 GMT
• Title: Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems
• Authors: Hironori Makino
• Abstract summary: We investigate energy level statistics of a bounded quantum system, whose classical dynamical system exhibits bifurcations. The spike oscillations of the two-point correlation function (TPCL) are analyzed by the reduced chi-squared value which deduced to exhibit abrupt increases at bifurcation points. Using this method, we attempt to numerically detect the bifurcation points of a lemon-shaped billiard.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Energy level statistics of a bounded quantum system, whose classical dynamical system exhibits bifurcations, is investigated using the two-point correlation function (TPCL), which at the bifurcation points exhibits periodic spike oscillations owing to the accumulation of levels called the shell effect. The spike oscillations of the TPCL is analyzed by the reduced chi-squared value which deduced to exhibit abrupt increases at bifurcation points, thereby yielding a novel detection approach. Using this method, we attempt to numerically detect the bifurcation points of a lemon-shaped billiard.

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