Search

Size dependence of vacancy migration energy in ionic nano particles is investigated by analysis of potential energy surfaces in potassium chloride clusters. Numerical methods are used to find almost all local minima and transition states for vacancy migration in clusters of different sizes, and reveal characteristic features of energy surface structure. It is shown that migration energy is significantly lower near a cluster surface than near a cluster core, and the mean first-passage time for migration of a vacancy decreases with cluster size. These results are consistent with observations of high diffusion rates in small clusters.

An isoenergetic molecular dynamics simulation is done to investigate two fundamental atomistic mechanisms responsible for rapid diffusion in nanoclusters. Using a semi-empirical potential we successfully reproduce the so-called Spontaneous Alloying and Spontaneous Mixing phenomena, which have been found in experiments for bimetallic and ternary alkali halide clusters, respectively. We found that a novel mechanism, named here the Surface Peeling Mechanism, is of primary importance for Spontaneous Alloying, while the Vacancy Mechanism is dominant in Spontaneous Mixing. We also show that the dominant mechanism responsible for rapid diffusion is related to the size dependence of vacancy formation energy.

A new semiclassical mechanism of multi-dimensional tunneling, which originates in the complexified stable and unstable manifolds of the unstable saddle (or unstable periodic orbit) on top of the potential barrier, causes a remarkable plateau-like structure in the tunneling spectrum. Such a mechanism is very universal and works when the instanton mechanism breaks down due to the strong coupling between the degrees of freedom.

We numerically investigate quantum diffusion of the initially localized wave packet in kicked one-dimensional disordered system (1DDS) with classical coherent perturbation. The wave packet localizes in the unperturbed kicked Anderson model. On the other hand, it diffuses obeying subdiffusion or normal diffusion law by coupling with coherent perturbation consisting of a few frequency components. We call the state “dynamically delocalized state”. We give the perturbation strength dependence of the diffusion rate. Moreover, it is numerically shown that in the subdiffusive cases the corresponding space (n)–time (t) distribution functions are characterized by a unified scaling form P(n,t)∝exp{−const(|n|/tα/2)β} ( 0⩽α⩽1, 1⩽β⩽2 ) concerning the space–time indexes (α,β). It is also shown that an universal relation β=2/(2−α) works on the delocalization in the perturbed kicked Anderson model.

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.

A simple algorithm of velocity scaling is proposed for the isothermal simulation of nonequilibrium relaxation processes accompanied with heat generation or absorption. The algorithm controls the kinetic temperature averaged over an arbitrary time interval at an arbitrary relaxation rate and at an arbitrary velocity scaling interval. The general conditions of controlling temperature are derived analytically and criteria for stable control are established. Our algorithm is applied to simulating the effect of substrate on the “spontaneous alloying” process of metal microclusters [H. Yasuda, H. Mori, M. Komatsu, K. Takeda, and H. Fujita, J. Electron Microsc. 41, 267 (1992)]. The results are compared with the results obtained by the Langevin algorithm in which the kinetic energy of every atom is controlled by respective stochastic heat reservoir. In spite of the marked difference between the two algorithms the relaxation dynamics agree very well in quantity over a sufficient wide range of control parameters.

A divergent movement exhibited by singularities of complexified classical trajectories plays an important role in multi-dimensional barrier tunneling. It induces a complex-domain heteroclinic entanglement between the stable manifold of a barrier-top unstable periodic orbit and incoming trajectories. Formation of such a complexified dynamical structure is generic in multi-dimensional barrier systems and enables multiple tunneling paths to contribute to the tunneling phenomena, which is observed as a “fringed” tunneling phenomenon, i.e., the tunneling probability is remarkably fringed due to the interference among multiple tunneling paths.

Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In a stronger perturbation regime, the tunneling component of the wave-matrix exhibits a remarkable interference fringes, which is clarified by the semiclassical theory as an interference among multiple complex tunneling trajectories. It turns out that such a peculiar behavior is the manifestation of an intrinsic multi-dimensional effect closely related to a singular movement of singularities possessed by the complex classical trajectories.

“Spontaneous alloying” observed by Yasuda, Mori et al. for metallic small clusters is simulated using classical Hamiltonian dynamics. Very rapid alloying occurs homogeneously and cooperatively starting from the solid phase of the cluster if the heat of solution is negative and the size of cluster is less than a critical size. Analysis of 2D models reveals that the alloying rate obeys an Arrhenius-type law, which predicts the alloying time much less than second at room temperature. Evidences manifesting that the spontaneous alloying proceeds in the solid phase without melting are also presented. The simulation reproduces the essential features of the experiments.

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.

The role of diffraction is investigated for two-dimensional area-preserving maps with sharply or almost sharply divided phase space, in relation to the issue of dynamical tunneling. The diffraction effect is known to appear in general when the system contains indifferentiable or discontinuous points. We find that it controls the quantum transition between regular and chaotic regions in mixed phase space in the case where the border between these regions is set to be sharp. However, its manifestation is rather subtle: it would be possible to identify the diffraction effect under suitable coordinates if the support of the wave function contains indifferentiable or discontinuous points, whereas it is mixed with the tunneling effect and the whole process becomes hybrid if the support does not contain the sources of diffraction. We make detailed analyses, including the semiclassical treatment of edge contributions of the one-step propagator, to clarify the nature of diffraction in mixed phase space. Our result implies that chaos does not play any roles in the regular-to-chaotic transition process when the phase space is sharply divided.

Tunneling essentially different from instanton-type tunneling, say noninstanton tunneling, is studied from both semiclassical and quantum viewpoints. Taking a periodically perturbed rounded-off step potential for which the instanton-type tunneling is substantially prohibited, we analyze change of the tunneling probability with change of the perturbation frequency based on the stable-unstable manifold-guided tunneling (SUMGT) theory, which we have recently introduced. In the large and small limits of the frequency, the tunneling rate rapidly decays, but it is markedly enhanced in an intermediate range. We will also make a quantum interpretation of the noninstanton tunneling by using an exactly solvable model---a periodically perturbed right-angled step potential. Analysis with this model shows that SUMGT is considered as a sort of photoassisted tunneling through a large energy gap induced with absorbing a huge number quanta, which is completely different from the instanton-type tunneling. Both approaches from the semiclassical and quantum viewpoints complement each other to cause a better understanding of noninstanton tunneling.

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.

It is shown that stable and unstable manifolds in the complex plane control dynamical tunneling in mixed systems. Some hypotheses based upon numerical observations combined with recent results in the theory of complex dynamical systems (Bedford and Smillie 1991, 1992) reveal that the stable manifolds in complex space are densely distributed in the set of tunneling orbits which asymptotically contribute to the semiclassical propagator. It is indeed verified that the tunneling amplitude out of the KAM region is well reproduced by the orbits attracted by unstable periodic orbits in the real phase space.