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A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom $M+1$ is regarded as the spatial dimension $d$, but the critical dimension is not $d=M+1-2$ of the ordinary AT but $d=3$., Comment: 5 pages, 4 figures

Following the paper exploring the Anderson localization of monochromatically perturbed kicked quantum maps [Phys.Rev. E{\bf 97},012210], the delocalization-localization transition phenomena in polychromatically perturbed quantum maps (QM) is investigated focusing particularly on the dependency of critical phenomena upon the number $M$ of the harmonic perturbations, where $M+1=d$ corresponds to the spatial dimension of the ordinary disordered lattice. The standard map and the Anderson map are treated and compared. As the basis of analysis, we apply the self-consistent theory (SCT) of the localization, taking a plausible hypothesis on the mean-free-path parameter which worked successfully in the analyses of the monochromatically perturbed QMs. We compare in detail the numerical results with the predictions of the SCT, by largely increasing $M$. The numerically obtained index of critical subdiffusion $t^\alpha$~($t$:time) agrees well with the prediction of one-parameter scaling theory $\alpha=2/(M+1)$, but the numerically obtained critical exponent of localization length significantly deviates from the SCT prediction. Deviation from the SCT prediction is drastic for the critical perturbation strength of the transition: if $M$ is fixed the SCT presents plausible prediction for the parameter dependence of the critical value, but its value is $1/(M-1)$times smaller than the SCT prediction, which implies existence of a strong cooperativity of the harmonic perturbations with the main mode., Comment: 15 pages, 14 figures

Relaxation modes are the collective modes in which all probability deviations from equilibrium states decay with the same relaxation rates. In contrast, a first passage time is the required time for arriving for the first time from one state to another. In this paper, we discuss how and why the slowest relaxation rates of relaxation modes are reconstructed from the first passage times. As an illustrative model, we use a continuous-time Markov state model of vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all characteristics of the relaxations in KCl nanoclusters come from the fact that they are hybrids of two kinetically different regions of the fast surface and slow bulk diffusions. The origin of the different diffusivities turns out to come from the heterogeneity of the activation energies on the potential energy landscapes. We also develop a stationary population method to compute the mean first passage times as mean times required for pair annihilations of particle-hole pairs, which enables us to obtain the symmetric results of relaxation rates under the exchange of the sinks and the sources. With this symmetric method, we finally show why the slowest relaxation times can be reconstructed from the mean first passage times., Comment: 8 figures

A renormalized perturbation method is developed for quantum maps of periodically kicked rotor models to study the tunneling effect in the nearly integrable regime. Integrable Hamiltonians closely approximating the nonintegrable quantum map are systematically generated by the Baker-Hausdorff-Campbell (BHC) expansion for symmetrized quantum maps. The procedure results in an effective integrable renormalization, and the unrenormalized residual part is treated as the perturbation. If a sufficiently high-order BHC expansion is used as the base of perturbation theory, the lowest order perturbation well reproduces tunneling characteristics of the quasibound eigenstates, including the transition from the instanton tunneling to a noninstanton one. This approach enables a comprehensive understanding of the purely quantum mechanisms of tunneling in the nearly integrable regime. In particular, the staircase structure of tunneling probability dependence on quantum number can be clearly explained as the successive transition among multiquanta excitation processes. The transition matrix elements of the residual interaction have resonantly enhanced invariant components that are not removed by the renormalization. Eigenmodes coupled via these invariant components form noninstanton (NI) tunneling channels of two types contributing to the two regions of each step of the staircase structure: one type of channel is inside the separatrix, and the other goes across the separatrix. The amplitude of NI tunneling across the separatrix is insensitive to the Planck constant but shows an essentially singular dependence upon the nonintegrablity parameter. Its relation to the Melnikov integral, which characterizes the scale of classical chaos emerging close to the saddle on the potential top, is discussed.

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.

Graphs of the most probable transitions for a transition probability matrix, $e^{\tau K}$, i.e., the time evolution matrix of the transition rate matrix $K$ over a finite time interval $\tau$, are considered. We study how the graph structures of the most probable transitions change as functions of $\tau$, thereby elucidating that a kinetic threshold $\tau_g$ for the graph structures exists. Namely, for $\tau, Comment: 8 figures

The Stokes geometry for the propagator of the quantum Henon map is studied in the light of recent developments of the exact WKB analysis. As the simplest possible situation the Henon map satisfying the so-called horseshoe condition is closely analyzed, together with listing up local bifurcation patterns of the Stokes geometry. This is exactly in the same spirit as pruning theory for the classical horseshoe system, and the present paper is placed as the first step to establish pruning theory of the Stokes geometry for chaotic systems. Our analysis reveals that the birth and death of the WKB solutions caused by the Stokes phenomenon do not occur in a local but entirely global manner, reflecting topological nature encoded in the Stokes geometry. We derive an explicit general formula to enumerate the number of WKB solutions in the asymptotic region and obtain its growth rate, which is shown to be less than the topological entropy of the corresponding classical dynamics. The relations to the diffraction catastrophe integrals and one-step multiply folding maps are also discussed.

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009)] and a Jacobi method. We test the method on a illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al. Chem. Phys. Lett. 654, 52 (2016)], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes., 5 pages, 3 figures

Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical wavepacket propagation. Some phenomenological formula of the dynamical localization length valid for wide range of control parameters are proposed for both SM and AM. For SM the formula completely agree with the experimentally established formula, and for AM the presence of a new regime of localization is confirmed. These formula can be derived by the self-consistent mean-field theory of Anderson localization on the basis of a new hypothesis for cut-off length. Transient diffusion in the large limit of the localization length is also discussed., 15 pages, 11 figures

The aim of this study is to examine some numerical tests of Padé approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole and the essential singularity can be characterized by the poles of the Padé approximation. However, it was not fully clear how the Padé approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the poles and zeros of the Padé approximated functions are alternately lined along the branch cut if the test function has branch cut, and poles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously have a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise also appear around the unit circle in the Padé approximation. It is also shown that the residue calculus for the Padé approximated functions can be used to confirm the numerical accuracy of the Padé approximation and quasianalyticity of the random power series.

As an application of the classically decayable correlation in a quantum chaos system maintained over an extremely long time-scale (Matsui et al, Europhys.Lett. 113(2016),40008), we propose a minimal model of quantum damper composed of a quantum harmonic oscillator (HO) weakly interacting with a bounded quantum chaos system. Although the whole system obeys unitary evolution dynamics of only three quantum degrees of freedom, the mechanical work applied to the HO is stationary converted into the "internal energy" characterized by an effective temperature in an irreversible way over a sufficiently long time-scale, if the components of the quantum chaos system are mutually entangled enough. A paradoxical dependence of the duration time of the stationary conversion on the driving strength is also discussed., Comment: 10 pages, 4 figures

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.

The Stokes geometry for the propagator of the quantum Henon map is studied. Virtual turning points and new Stokes curves, which have been proposed as entirely new notions appearing only in higher-order differential equations, are defined through deriving a set of differential equations acting on the propagator. A concrete recipe to construct Stokes geometry is presented and its validity is examined using three independent methods. The tree-pruning rule, a phenomenological scheme to cope with the complex WKB description of chaotic systems, is also examined in the light of the exact WKB treatment of the Stokes phenomenon.

To elucidate the atomistic diffusion mechanism responsible for the rapid diffusion in alkali halide nano particles, called Spontaneous Mixing, we execute molecular dynamics simulations with empirical models for KCl-KBr, NaCl-NaBr, RbCl-RbBr and KBr-KI. We successfully reproduce essential features of the rapid diffusion phenomenon. It is numerically confirmed that the rate of the diffusion clearly depends on the size and temperature of the clusters, which is consistent with experiments. A quite conspicuous feature is that the surface melting and collective motions of ions are inhibited in alkali halide clusters. This result indicates that the Surface Peeling Mechanism, which is responsible for the spontaneous alloying of binary metals, does not play a dominant role for the spontaneous mixing in alkali halide nanoclusters. Detailed analysis of atomic motion inside the clusters reveals that the Vacancy Mechanism is the most important mechanism for the rapid diffusion in alkali halide clusters. This is also confirmed by evaluation of the vacancy formation energy: the formation energy notably decreases with the cluster size, which makes vacancy formation easier and diffusion more rapid in small alkali halide clusters., Comment: 12 pages, 14 figures

The formation of the plateau spectrum is a manifestation of the classical unstable manifold in multi-dimensional barrier tunneling, for which contributing tunneling trajectories are guided by the stable and unstable manifolds in the complex domain. In this paper, we numerically confirm that the plateau spectrum is generally observed for a wide class of multi-dimensional barrier potentials. The results of complex semiclassical analysis are also discussed.

Multi-mode lasing in stadium-shaped cavities which are rigorously known to be fully chaotic is investigated both theoretically and experimentally. By a nonlinear dynamical model, it is shown that there exist multi-attractors of limit cycles and chaos corresponding to the final lasing states for large microstadiums. We also show that the envelopes of the far field patterns of the actual microstadium laser diodes are excellently approximated by fully chaotic ray-dynamics.

Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of critical phenomena, which depends on the number of frequency component $M$, is demonstrated. Diffusion exponents agree with theoretical prediction for the transition, but the critical exponent of the localization length deviates from it with increase in the $M$. The critical power $\epsilon_c$ of the normalized perturbation at the transition point remarkably decreases as $\epsilon_c \sim (M-1)^{-1}$., Comment: 6 pages, 5 figures

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.

Recent studies on complex dynamical systems in more than one dimension have revealed that even if the real phase space is a mixture of KAM tori and chaotic seas there exists a unique ergodic measure in the complex phase space which is (weakly) hyperbolic and gives maximal entropy of the dynamics. We present several pieces of numerical evidence and speculations on the existence of rotational domains in the complex space, implying that the measure thus obtained satisfies desired properties of the support of semiclassical wavefunctions in the mixed phase space.

In recent papers we demonstrated a new class of barrier tunneling phenomena which can be observed in periodically driven one dimensional barrier systems (i.e., 1.5D barrier tunneling systems). In such systems the tunneling component is in general accompanied by remarkable interference fringe patterns as the perturbation strength exceeds a certain characteristic value. Such a phenomenon is quite general and is not restricted to periodically driven 1D systems, and it may be also observed in intrinsic two dimensional autonomous systems. The complex-domain semiclassical theory developed by ourselves was applied to the problem, and we succeeded in reconstructing every detail of the fringed tunneling wavefunction only by using the complexified classical tunneling trajectories. This fact greatly motivates us to investigate the mechanism of the tunneling in terms of “classical mechanics”. The later part of the present paper is devoted to asserting the generality of the “classical mechanism” of the fringed tunneli...

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.

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton accompanied by spikes. We further introduce renormalized integrable Hamiltonians, and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely. It is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases. This also explains the reason why the staircase does not appear in the completely integrable system.

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.

The tunneling effect in multidimensional systems may be greatly influenced by the underlying chaotic dynamics which is generic in more than one-dimensional systems. Aiming at a classical dynamical description of chaotic tunneling, we have developed in the present paper a basic formulation for the complex-domain semiclassical wave-matrix of systems with 1.5 degrees of freedom, namely, periodically time-dependent 1D-scattering systems, which can be regarded as a minimal model of multidimensional systems. Using an autonomous 2D system equivalent to the periodically time-dependent system, the semiclassical expression of the wave-matrix described in the 1D time-dependent picture is derived. In the latter half of the paper, our semiclassical formulation is examined with two simple examples, i.e., an oscillating wall and an oscillating barrier. The semiclassical wave-matrix is constructed, paying particular attention to some problems which emerge by extending classical dynamics to complex domain, and the results are compared with the fully quantum counterparts. The semiclassical results agree quite well with the corresponding quantal results if complex classical trajectories are fully taken into account. The relationship between the semiclassical wave-matrix and Miller's classical S-matrix is also discussed.

Chaotic tunneling occurring in the standard map, which is one of the most familiar paradigms in simple chaotic mappings, is analyzed in terms of complex semiclassical theory in the time domain. It is shown that the complex classical trajectories successfully describe the transition to the region where the real classical path cannot reach. In connection with our previous result (Physica D115 (1998), 234), the universality of the organizing rule to find out dominantly contributing complex paths is suggested. Several fundamental problems in the treatment of semiclassical theory in the complex domain are also discussed.

The stationary lasing of the modes in a microdisk is formulated as a nonlinear eigenvalue problem for a nonlinear Maxwell equation. It is shown that whispering gallery modes can be obtained as stationary lasing solutions with finite pumping thresholds. Further, it is discovered that whispering gallery lasing modes can exist even though the angle of incidence to the disk boundary is smaller than the critical angle for total internal reflection.

Effect of dynamical perturbation on quantum localization phenomenon in one-dimensional disordered quantum system is investigated systematically by a numerical method. The dynamical perturbation is modeled by an oscillatory driving force containing M-independent (mutually incommensurate) frequency components. For M⩾2 a diffusive behavior emerges and the presence of finite localization length can no longer be detected numerically. The diffusive motion obeys a subdiffusion law characterized by the exponent α as ξ(t)2∝tα, where ξ(t)2 is the mean square displacement of the wave packet. With increase in M and/or the perturbation strength, the exponent α approaches rapidly to 1 which corresponds to the normal-diffusion. Moreover, the space(x)-time(t) dependence of the distribution function P(x,t) is reduced to a scaled form decided by α and an another exponent β such that , which contains the two extreme limits, i.e., the localization limit (α=0,β=1) and the normal-diffusion limit (α=1,β=2) in a unified manner.

“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.

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.

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.

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.

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.

Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and so on. We examine Pade approximation and some complementary methods to investigate the complex-analytical properties of some complex quantum states such as impurity states, Anderson-localized states and localized states of Harper model. The impurity states can be characterized by simple poles of the Pade approximation, and the localized states of Anderson model and Harper model can be characterized by an accumulation of poles and zeros of the Pade approximated function along a critical border, which implies a natural boundary (NB). A complementary method based on shifting the expansion-center is used to confirm the existence of the NB numerically, and it is strongly suggested that the both Anderson-localized state and localized states of Harper model have NBs in the complex extension. Moreover, we discuss an interesting relationship between our research and the natural boundary problem of the potential function whose close connection to the localization problem was discovered quite recently by some mathematicians. In addition, we also examine the usefulness of the Pade approximation for numerically predicting the existence of NB by means of two typical examples, lacunary power series and random power series., Comment: 19 pages, 20 figures

The relation between the degree of entanglement and time scale of time-irreversible behavior is investigated for classically chaotic quantum coupled kicked rotors by comparing the entanglement entropy (EE) and the lifetime of correspondence with classical decay of correlation, which was recently introduced. Both increase {\it on average} drastically with a strong correlation when the strength of coupling between the kicked rotors exceeds a certain threshold. The EE shows an anomalously large fluctuation resembling a critical fluctuation around the threshold value of coupling strength where the entanglement sharply increases toward full entanglement. In this regime it can be shown that, although the correlation is hidden, EE and the lifetime of {\it individual eigenfunctions} also have a positive correlation that can be seen via an another measure., 5 pages, 3 figures

The invariant torus of nonintegrable systems breaks up in complexified phase space. The breaking border is expected to form a natural boundary (NB) along which singularities are densely condensed. The NB cuts off the instanton orbit controlling the tunneling transport from a quantized invariant torus, which might result in a serious effect on the tunneling process. In the present Letter, we provide clear evidence showing that the presence of the NB is observable as an anomalous enhancement of the tunneling wave amplitude in the immediate outer side of the NB.

In multidimensional barrier tunneling, there exist two different types of tunneling mechanisms, instanton-type tunneling and noninstanton tunneling. In this paper we investigate transitions between the two tunneling mechanisms from the semiclassical and quantum viewpoints taking two simple models: a periodically perturbed Eckart barrier for the semiclassical analysis and a periodically perturbed rectangular barrier for the quantum analysis. As a result, similar transitions are observed with change of the perturbation frequency $\ensuremath{\omega}$ for both systems, and we obtain a comprehensive scenario from both semiclassical and quantum viewpoints for them. In the middle range of $\ensuremath{\omega}$, in which the plateau spectrum is observed, noninstanton tunneling dominates the tunneling process, and the tunneling amplitude takes the maximum value. Noninstanton tunneling explained by stable-unstable manifold guided tunneling (SUMGT) from the semiclassical viewpoint is interpreted as multiphoton-assisted tunneling from the quantum viewpoint. However, in the limit $\ensuremath{\omega}\ensuremath{\rightarrow}0$, instanton-type tunneling takes the place of noninstanton tunneling, and the tunneling amplitude converges on a constant value depending on the perturbation strength. The spectrum localized around the input energy is observed, and there is a scaling law with respect to the width of the spectrum envelope, i.e., the width $\ensuremath{\propto}\ensuremath{\hbar}\ensuremath{\omega}$. In the limit $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, the tunneling amplitude converges on that of the unperturbed system, i.e., the instanton of the unperturbed system.

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.

In quantum map systems exhibiting normal diffusion, time-reversal characteristics converge to a universal scaling behavior which implies a prototype of irreversible quantum process [H.S. Yamada, K.S. Ikeda, Eur. Phys. J. B 85, 41 (2012)]. In the present paper, we extend the investigation of time-reversal characteristic to time-continuous quantum systems which show normal diffusion. Typical four representative models are examined, which is either deterministic or stochastic, and either has or not has the classical counterpart. Extensive numerical examinations demonstrate that three of the four models have the time-reversal characteristics obeying the same universal limit as the quantum map systems. The only nontrivial counterexample is the critical Harper model, whose time-reversal characteristics significantly deviates from the universal curve. In the critical Harper model modulated by a weak noise that does not change the original diffusion constant, time-reversal characteristic recovers the universal behavior.

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.

Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of the systems, there exist a universal minimal quantum threshold above which the system completely loses the past memory, and the time-reversed dynamics as well as the time-reversal characteristics asymptotically trace universal curves independent of the details of the systems., Comment: 4 pages, 4 figures

The aim of this paper is twofold: one is to give a detailed description of an alternative graph-based analysis method, which we call saddle connectivity graph, for analyzing the global topography and the dynamical properties of many-dimensional potential-energy landscapes and the other is to give examples of applications of this method in the analysis of the kinetics of realistic systems. A Dijkstra-type shortest path algorithm is proposed to extract dynamically dominant transition pathways by kinetically defining transition costs. The applicability of this approach is first confirmed by an illustrative example of a low-dimensional random potential. We then show that a coarse-graining procedure tailored for saddle connectivity graphs can be used to obtain the kinetic properties of 13- and 38-atom Lennard-Jones clusters. The coarse-graining method not only reduces the complexity of the graphs, but also, with iterative use, reveals a self-similar hierarchical structure in these clusters. We also propose that the self-similarity is common to many-atom Lennard-Jones clusters.

In multidimensional barrier tunneling, there exist different semiclassical mechanisms, i.e., the well-established instanton mechanism and the recently discovered mechanism utilizing complexified stable-unstable manifolds as the guide of tunneling paths. We demonstrate that the transition between the two mechanisms can be observed as a remarkable change in the spectrum of tunneled particles and propose a practical method to evaluate the tunneling rates of the two mechanisms.

We investigate numerically and analytically the effects of conservation of total translational and angular momentum on the distribution of kinetic energy among particles in microcanonical particle systems with small number of degrees of freedom, specifically microclusters. Molecular dynamics simulations of microclusters with constant total energy and momenta, using Lennard-Jones, Morse, and Coulomb plus Born-Mayer-type potentials, show that the distribution of kinetic energy among particles can be inhomogeneous and depend on particle mass and position even in thermal equilibrium. Statistical analysis using a microcanonical measure taking into account of the additional conserved quantities gives theoretical expressions for kinetic energy as a function of the mass and position of a particle with only O(1/N;{2}) deviation from the Maxwell-Boltzmann distribution. These expressions fit numerical results well. Finally, we propose an intuitive interpretation for the inhomogeneity of the kinetic energy distributions.

We discuss the recent progress in the theoretical study on ionization processes of rare-gas atoms in strong optical fields, in atomic physics and in nonlinear dynamics. Special emphasis is placed on using the notion of trajectories in the study, which are particular Feynman paths in quantum mechanics. In terms of trajectories, both mechanisms of tunnel ionization and chaotic ionization are explained, and a clear difference is made between them. A possible experimental setting is discussed to observe the crossover of the two ionizations.

A very weakly coupled linear oscillator is proposed as a detector for observing time-irreversible characteristics of a quantum system, and it is used to measure the lifetime during which a classically chaotic quantum system shows decay of correlation. Except for a particular case where the lifetime agrees with the conventional Heisenberg time, which is proportional to the Hilbert space dimension $N$, it is in general much longer: the lifetime increases in proportion to the product of $N$ and the number of superposed eigenstates, and is proportional to $N^2$ in the case of full superposition., Comment: 6 pages, 2 figures. arXiv admin note: text overlap with arXiv:1510.00199