arXiv subjects

Hironori Makino

Publications and source records attributed to Hironori Makino.

4 recordsLinked to original sources

arXiv2022

Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems

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.

nlin.CD↗

arXiv2022

E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach

Theory of the quantal level statistics of classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV)\cite{MT03,MMT09}, is successfully extended to the study of $E(K,L)$ function which constitutes a fundamental measure to determine most statistical observables of quantal levels in addition to LSD and LNV. In the theory of Makino et al., the eigenenergy level is regarded as a superposition of infinitely many components whose formation is supported by the Berry-Robnik approach in the far semiclassical limit\cite{Robn1998}. We derive the limiting $E(K,L)$ function in the limit of infinitely many components and elucidates its properties when energy levels show deviations from the Poisson statistics.

nlin.CD↗

arXiv2022

Bifurcation and anomalous spectral accumulation in oval billiard

Spectral statistics of quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF) which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at bifurcation point is found to show anomalous accumulation which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space, which contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller trace formula.

nlin.CD↗

arXiv2008

Brownian Motion Captured with a Self-Mixing Laser

We measured the overall motion of Brownian particles suspended in water by a self-mixing thin-slice solid-state laser with extreme optical sensitivity. From the demodulated signal of laser intensity fluctuations through self-mixing modulations by the interference between the lasing field and Doppler-shifted scattered fields from Brownian particles, it was found that the changes over time in random walks of small particles suspended in water result in different overall dynamics when the field of vision for particles seen by the laser beam (scale of the observation) is changed. At a small focal volume of the laser beam, in which the relevant diffusion broadening is observed, the overall motion which can be represented by the motion of a ''virtual'' single particle whose velocity obeys a double-peaked non-Gaussian distribution function. The fast motion of a virtual particle, featuring fractional Brownian motion, which leads to a pure random walk with increasing the observation time, has been characterized in terms of mean-square displacements of a virtual particle.

physics.optics↗