Hironori Makino

Net motion of an ensemble of many Brownian particles captured with a self-mixing laser

The overall dynamics of Brownian particles suspended in water were captured with high time resolution by using a self-mixing thin-slice solid-state laser. The net motion of an ensemble of many particles moving in the small imaging field observed at given time intervals was found to be represented by Brownian motions of an effective medium obeying the Ornstein–Uhlenbeck process, whose physical parameters have scaling relations with those of a real turbid medium. An approach toward measuring particle diffusion constants is described.

Irregular lasing pattern formation and dynamic effects in a thin-slice solid-state laser.

We found an abrupt transverse-mode transition from an irregular to a Gaussian lasing pattern or billiard-like lasing patterns with increasing the pump power in a laser-diode-pumped thin-slice Nd:GdVO4 laser with coated dielectric mirrors on both ends. A variety of irregular stationary lasing patterns were observed with a slight change in the pump position due to polished crystal surface roughness and ineffective lasing field confinement in transverse directions. A physical interpretation for observed irregular patterns was given in terms of wave formations in gradient refractive index lens with undulated reflective end surfaces. Intensity modulation of the laser, resulting from the interference of non-orthogonal transverse mode pairs embedded in the irregular lasing patterns, and associated rich chaotic pulsations were demonstrated. Observed nonlinear dynamics were well reproduced by numerical simulation.

Transverse effects in a microchip laser with asymmetric end-pumping: modal interference and dynamic instability

Formation of complicated emission patterns consisting of many transverse modes and associated intensity pulsations at beat frequencies between some pairs of transverse eigenmodes in microchip solid-state lasers with laser-diode asymmetric end-pumping are reviewed. The dependence of billiard-like transverse patterns on pump power and crystal rotation (i.e. kaleidoscopic patterns) was demonstrated in a 0.3 mm thick thin-slice LiNdP4O12 laser with sheet-like end-pumping. Pump-power-dependent high-speed self-pulsations were observed. The asymmetric optical confinement resulted in the formation of transverse patterns which were totally different from normal Hermite–Gaussian resonator modes. The interference among pairs of non-orthogonal transverse eigenmode fields, whose energy levels exhibited avoided crossing with increasing pump power, was shown to result in high-speed intensity modulations. A good numerical reproduction of the observed high-speed modulations was obtained with model equations.

Statistical properties of spectral fluctuations for a quantum system with infinitely many components.

Extending the idea formulated in Makino {\it{et al}}[Phys.Rev.E {\bf{67}},066205], that is based on the Berry--Robnik approach [M.V. Berry and M. Robnik, J. Phys. A {\bf{17}}, 2413], we investigate the statistical properties of a two-point spectral correlation for a classically integrable quantum system. The eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit. We derive the level number variance (LNV) in the limit of infinitely many components and discuss its deviations from Poisson statistics. The slope of the limiting LNV is found to be larger than that of Poisson statistics when the individual components have a certain accumulation. This property agrees with the result from the semiclassical periodic-orbit theory that is applied to a system with degenerate torus actions[D. Biswas, M.Azam,and S.V.Lawande, Phys. Rev. A {\bf 43}, 5694].

Self-induced high-speed modulation in microchip solid-state lasers with asymmetric end pumping

We applied laser-diode sheetlike end pumping to a multimode Nd:YVO(4) laser and observed high-speed (>400-MHz) modulation of the intensity of chaotic pulsation near 1 MHz. The frequencies of modulation were the beat frequencies for pairs of closely spaced lasing modes. Asymmetric optical confinement and the resultant modal interference are shown to lead to oval-hollow-mode operation in which modal beat notes induce high-speed modulation, the frequency range of which is 2 orders of magnitude higher than the intrinsic relaxation oscillation frequency. Good numerical reproduction of the observed chaotic pulsations and their high-speed modulation was obtained with model equations in which such effects as nonlinear gain coupling among modes and field interference between pairs of modes were included. High-speed pulsations in nonchaotic lasers were also demonstrated.

Quantum Chaos and Randomness

In contrast to the classical Hamiltonian mechanics whose chaotic behaviors are now well established, quantum mechanics is still obscure about the origin of its random behavior. It is shown in this ...

Deviations from Berry-Robnik Distribution Caused by Spectral Accumulation

By extending the Berry--Robnik approach for the nearly integrable quantum systems,\cite{[1]} we propose one possible scenario of the energy level spacing distribution that deviates from the Berry--Robnik distribution. The result described in this paper implies that deviations from the Berry--Robnik distribution would arise when energy level components show strong accumulation, and otherwise, the level spacing distribution agrees with the Berry--Robnik distribution.By extending the Berry–Robnik approach for the nearly integrable quantum systems, we propose one possible scenario of the energy level spacing distribution that deviates from the Berry–Robnik distribution. The result described in this paper implies that deviations from the Berry–Robnik distribution would arise when energy level components show strong accumulation, and otherwise, the level spacing distribution agrees with the Berry–Rbnik distribution.

Long-Range Spectral Statistics of Classically Integrable Systems: Investigation along the Line of the Berry-Robnik Approach

Extending the argument of a previous paper [H. Makino and S. Tasaki, Phys. Rev. E 67 (2003), 066205] to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are obtained by applying the approach of Berry and Robnik [M. V. Berry and M. Robnik, J. of Phys. A 17 (1984), 2413] and the mathematical framework of Pandey [A. Pandey, Ann. of Phys. 119 (1979), 170] to systems with infinitely many components, and they are parameterized by a single function c, where c = 0 corresponds to Poisson statistics, and c ¬= 0 indicates deviations from Poisson statistics. This implies that even when the spectral components are statistically independent, non-Poissonian spectral statistics are possible.Extending the argument of Ref.\citen{[4]} to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are obtained by applying the approach of Berry and Robnik\cite{[0]} and the mathematical framework of Pandey \cite{[2]} to systems with infinitely many components, and they are parameterized by a single function

Stationary collective fluctuation in Brownian motions of particles within the limited field of vision

\bar{c}

Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach

, where