Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems

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.

Published: 23 August 2022, Progress of Theoretical and Experimental Physics, ptac111,

References in corpus (4)

• Semiclassical Foundation of Universality in Quantum Chaos
• Anomalous shell effect in the transition from a circular to a triangular billiard
• E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach
• Bifurcation and anomalous spectral accumulation in oval billiard

Cited by in corpus (1)

• Phenomenology of quantum eigenstates in mixed-type systems: lemon billiards with complex phase space structure