Kensuke S. Ikeda

Passive Exposure to Mobile Phones: Enhancement of Intensity by Reflection

In a recent Letter [J. Phys. Soc. Jpn. 71 (2002) 432], we reported a preliminary calculation and concluded that public exposure to mobile phones can be enhanced by microwave reflection in public spaces. In this paper, we confirm the significance of microwave reflection reported in our previous Letter by experimental and numerical studies. Furthermore, we show that “hot spots” often emerge in reflective areas, where the local exposure level is much higher than average. Such places include elevators, and we discuss other possible environments including trains, buses, cars, and airplanes. Our results indicate the risk of “passive exposure” to microwaves.

Chaotic tunneling: a remarkable manifestation of complex classical dynamics in non-integrable quantum phenomena

Abstract The tunneling phenomenon in chaotic systems is analyzed in terms of the complex semi-classical method in the time domain. In contrast to the tunneling paths in integrable systems, it is discovered that there exist a tremendous number of candidate complex branches ( Laputa branches ) which may contribute to the semi-classical propagator. The origin of a lot of characteristic structures observed in the tunneling tail in chaotic systems, which are completely absent in case of integrable systems, can fully be interpreted using such complex paths. In particular, we found a remarkable object forming chain-like structures ( Laputa chains ), which are hidden in the set of initial valuas displayed on the complex plane and they just generate a variety of structures in tunneling tails. The relationship between the tunneling tail and the structure of the Laputa chain is analyzed in detail. The candidate trajectories, however, contain non-physical non-contributing part as a manifestation of Stokes Phenomenon , and empirical rules on how to remove such non-contributing parts is also discussed. On the basis of the whole story constructed here, chaotic tunneling is proposed as a universal tunneling mechanism originating in the complicated structure of classical chaotic manifolds in the complex regime. Several questions arose in the present study, but not clarified yet, are also listed up in relation to the theories of complex semi-classical method and complex dynamical systems.

Spontaneous alloying in binary metal microclusters: A molecular dynamics study

Microcanonical molecular-dynamics study of spontaneous alloying (SA), which is a manifestation of fast atomic diffusion in a nanosized metal cluster, is done in terms of a simple two-dimensional binary Morse model. Important features observed by Yasuda and Mori are well reproduced in our simulation. The temperature dependence and size dependence of SA phenomena are extensively explored by examining long-time dynamics. The dominant role of negative heat of solution in completing SA is also discussed. We point out that a presence of melting surface induces the diffusion of core atoms even if they are solidlike. In other words, the surface melting at substantially low temperature plays a key role in attaining SA.

Julia set describes quantum tunnelling in the presence of chaos

We find that characteristics of quantum tunnelling in the presence of chaos can be regarded as a manifestation of the Julia set of the complex dynamical system. Several numerical pieces of evidence for the standard map, together with a rigorous statement for the Henon map, are presented, demonstrating that the complex classical paths which contribute to the semiclassical propagator are dense in the Julia set. Chaotic tunnelling can thus be characterized by the transitivity of the dynamics and high density of the trajectories on the Julia set.

APPLICATION OF SYMPLECTIC INTEGRATOR TO STATIONARY REACTIVE-SCATTERING PROBLEMS : INHOMOGENEOUS SCHRODINGER EQUATION APPROACH

The FFT-symplectic integrator (SI) scheme devised for solving the wave packet propagation problem is applied to stationary reactive-scattering problems. In order to relate the stationary problem to the time-dependent problem, a class of Schrodinger equation with an inhomogeneous wave source term is introduced. By using the equivalence between the stationary scattering eigenstate and the equilibrium state of the inhomogeneous Schrodinger equation, the scattering eigenstates can be computed by integrating the inhomogeneous Schrodinger equation with the FFT-SI scheme. A Gaussian wave source is proposed as an efficient wave source exhibiting rapid relaxation toward the eigenstate. Our method is tested by a one-dimensional example which has an analytical solution, and great numerical accuracy is confirmed. It is further examined by an example of time-dependent scattering and by a two-dimensional example of chaotic tunnel-scattering.

Anomalous diffusion and scaling behavior of dynamically perturbed one-dimensional disordered quantum systems

Abstract Coherent oscillatory perturbations enhance the localization length of one-dimensional quantum disordered systems to a numerically undetectable level and result in an anomalous diffusion. The transition to the normal diffusion occurs continuously with the perturbation strength and/or the number of frequency components of the oscillatory perturbation. The corresponding space(x)-time(t) distribution function P(x,t) reduces to the unified scaling form P(x,t) ∼ exp[−const × ( x t α 2 ) β ] , which contains the localization and the normal diffusion as two extreme cases and interpolates the two limits in the general case.

SPONTANEOUSLY INDUCED IRREVERSIBLE ENERGY TRANSPORT IN CLOSED ELECTRON-PHONON SYSTEMS

Abstract Energy relaxation dynamics associated with the electron scattering process is investigated with a simple fully quantum model of an electron-phonon system. It is numerically demonstrated that contrary to traditional theories infinite numbers of phonon modes are not necessary and just a few phonon modes are sufficient for an irreversible energy transfer from the scattered electron to the phonon modes to be induced if the scattering potential is spatially irregular. Moreover, the phonon mode reaches promptly a thermalized state characterized by a well-defined temperature. The possibility that such a process might be an origin of resistivity in a closed quantum system is discussed.

Julia sets and chaotic tunneling: II

The tunneling phenomenon in non-integrable systems is studied in the framework of complex semiclassical theory. Complex trajectories which dominate tunneling in the presence of chaos (chaotic tunneling) are investigated numerically for several quantum maps. The discovery of a characteristic structure in the initial value representation of tunneling trajectories, named the Laputa chain, is reviewed, and it is shown how trajectories starting from Laputa chains make the dominant contribution to the semiclassical calculation of the wavefunction in the chaotic regime. This supports the argument that Laputa chains play an important role in the fully complex-domain semiclassical description of chaotic tunneling. Further, numerical analysis shows that the Laputa chain has distinct asymptotic properties in the long time limit. In particular, it is shown that the imaginary action along the trajectories starting from the Laputa chain, which determines the contribution to the tunneling probability, tends to converge absolutely in the asymptotic limit. On the basis of these features, we propose an empirical definition of the Laputa chain which can provide a basis for further mathematical development. Moreover, a connection is pointed out between the asymptotic structure of Laputa chains and Julia sets manifest in asymptotic dynamics of complex maps. Based on these results, we make the conjecture that Julia sets play a fundamental role in the complex semiclassical dynamical theory of tunneling in non-integrable systems.

Nonlinear whispering-gallery modes in a microellipse cavity

We study theoretically the effect of deformed microelliptical cavities on lasing characteristics. We show that the transition of stationary lasing states from unidirectional rotational waves to a mixture of clockwise and anticlockwise rotational waves occurs when the shape of a disk is deformed to that of an ellipse.

Complex-classical mechanism of the tunnelling process in strongly coupled 1.5-dimensional barrier systems

The fringed tunnelling, which can be observed in strongly coupled 1.5-dimensional barrier systems as well as in autonomous two-dimensional barrier systems, is a manifestation of intrinsic multi-dimensional effects in the tunnelling process. In this paper, we investigate such an intrinsic multi-dimensional effect on the tunnelling by means of classical dynamical theory and semiclassical theory, which are extended to the complex domain. In particular, we clarify the underlying classical mechanism which enables multiple tunnelling trajectories to simultaneously contribute to the wavefunction, thereby resulting in the formation of the remarkable interference fringe on it. Theoretical analyses are carried out in the low-frequency regime based upon a complexified adiabatic tunnelling solution, together with the Melnikov method extended to the complex domain. These analyses reveal that the fringed tunnelling is a result of a heteroclinic-like entanglement between the complexified stable manifold of the barrier-top unstable periodic orbit and the incident beam set. Tunnelling particles reach the real phase plane very promptly, guided by the complexified stable manifold, which gives quite a different picture of the tunnelling from the ordinary instanton mechanism. More fundamentally, the entanglement is attributed to a divergent movement of movable singularities of the classical trajectory, namely, to a singular dependence of singularities on its initial condition.