Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems
arXiv:2208.09244 · doi:10.1093/ptep/ptac111
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.
arXiv commentPublished: 23 August 2022, Progress of Theoretical and Experimental Physics, ptac111,
References in corpus (14)
- Semiclassical Foundation of Universality in Quantum Chaos
- Bifurcations of Periodic Orbits and Uniform Approximations
- Classical and quantum chaos in a circular billiard with a straight cut
- Semiclassical Interpretation of the Mass Asymmetry in Nuclear Fission
- Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: I: Elliptic Billiard
- Classcial Bifurcation and Enhancement of Quantum Shells --- Systematic Analysis of Reflection-Asymmetric Deformed Oscillator ---
- Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-
- Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
- Periodic-Orbit Bifurcations and Superdeformed Shell Structure
- Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance
- Periodic-Orbit Bifurcation and Shell Structure in Reflection-Asymmetric Deformed Cavity
- 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