arXiv subjects

Kensuke S. Ikeda

Publications and source records attributed to Kensuke S. Ikeda.

At least 19 recordsLinked to original sources

arXiv2025

Quantum diffusion in the Harper model under polychromatic time-perturbation

Quantum dynamics of the Harper model with self-duality exhibits localized, diffusive, and ballistic states depending on the potential strength $V$. By adding time-dependent harmonic perturbations composed of $M$ incommensurate frequencies, we show that all states of the Harper model transition to quantum diffusive states as the perturbation strength $ε$ increases for $M \geq 3$. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the $(ε,V)$ parameter space is presented.

cond-mat.dis-nn↗

arXiv2024

Dynamical tunneling across the separatrix

The strong enhancement of tunneling couplings typically observed in tunneling splittings in the quantum map is investigated. We show that the transition from instanton to noninstanton tunneling, which is known to occur in tunneling splittings in the space of the inverse Planck constant, takes place in a parameter space as well. By applying the absorbing perturbation technique, we find that the enhancement invoked as a result of local avoided crossings and that originating from globally spread interactions over many states should be distinguished and that the latter is responsible for the strong and persistent enhancement. We also provide evidence showing that the coupling across the separatrix in phase-space is crucial in explaining the behavior of tunneling splittings by performing the wave-function-based observation. In the light of these findings, we examine the validity of the resonance-assisted tunneling theory.

cond-mat.mes-hall↗

arXiv2024

Quantum Diffusion Induced by Small Quantum Chaos

It is demonstrated that quantum systems classically exhibiting strong and homogeneous chaos in a bounded region of the phase space can induce a global quantum diffusion. As an ideal model system, a small quantum chaos with finite Hilbert space dimension $N$ weakly coupled with $M$ additional degrees of freedom which is approximated by linear systems is proposed. By twinning the system, the diffusion process in the additional modes can be numerically investigated without taking the unbounded diffusion space into account explicitly. Even though $N$ is not very large, diffusion occurs in the additional modes as the coupling strength increases if $M \geq 3$. If $N$ is large enough, a definite quantum transition to diffusion takes place through a critical sub-diffusion characterized by an anomalous diffusion exponent.

cond-mat.stat-mech↗

arXiv2023

Localized-Diffusive and Ballistic-Diffusive Transitions in Kicked Incommensurate lattice

By using the kicked Harper model, the effect of dynamical perturbations to the localized and ballistic phases in aperiodic lattice systems is investigated. The transition from the localized phase to diffusive phase via a critical sub-diffusion $t^α$($t$:time) with $0<α<1$ is observed. In addition, we first confirmed the existence of the transition from the ballistic phase to the diffusive phase via a critical super-diffusion with $1<α<2$.

cond-mat.dis-nn↗

arXiv2022

Dynamical Localization and Delocalization in Polychromatically Perturbed Anderson Map

In the previous paper [PRE 101,032210(2020)], localization and delocalization phenomena in the polychromatically perturbed Anderson map (AM) were elucidated mainly from the viewpoint of localization-delocalization transition (LDT) on the increase of the perturbation strength $ε$. In this paper, we mainly investigate the dependency of the phenomena on the disorder strength $W$ ($W-$dependence) in the AM with a characteristic disorder strength $W^*$. In the completely localized region the $W-$dependence and $ε-$dependence of the localization length show characteristic behavior similar to those reported in monochromatically perturbed case [PRE 97,012210(2018)]. Furthermore, the obtained results show that even for the increase of the $W$, the critical phenomena and critical exponent are found to be similar to those in the LDT caused by the increase of $ε$. We also investigate the diffusive properties of the delocalized states induced by the parameters.

cond-mat.dis-nn↗

arXiv2022

Localization and delocalization properties in quasi-periodically perturbed Kicked Harper and Harper models

We numerically study the single particle localization and delocalization phenomena of an initially localized wave packet in the kicked Harper model (KHM) and Harper model subjected to quasi-periodic perturbation composed of $M-$modes. Both models are localized in the monochromatically perturbed case $M=1$. KHM shows localization-delocalization transition (LDT) above $M\geq2$ as increase of the perturbation strength $\eps$. In contrast, in a time-continuous Harper model with the perturbation, it is confirmed that the localization persists for $M=2$ and the LDT occurs for $M\geq 3$. Furthermore, we investigate the diffusive property of the delocalized wave packet in the KHM and Harper model for $\eps$ above the critical strength $\eps_c$ ($\eps>\eps_c$) comparing with other type systems without localization, which takes place a ballistic to diffusive transition in the wave packet dynamics as the increase of $\eps$.

cond-mat.dis-nn↗

arXiv2022

Localization and delocalization properties in quasi-periodically driven one-dimensional disordered system

Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the preliminary letter [PRE {\bf 103}, L040202(2021)]. We investigate in detail the localization-delocalization characteristics of the model with respect to three parameters: the disorder strength $W$, the perturbation strength $ε$ and the number of the colors $M$ which plays the similar role of spatial dimension. In particular, attentions are focused on the presence of localization-delocalization transition (LDT) and its critical properties. For $M\geq 3$ the LDT exists and a normal diffusion is recovered above a critical strength $ε$, and the characteristics of diffusion dynamics mimic the diffusion process predicted for the stochastically perturbed Anderson model even though $M$ is not large. These results are compared with the results of time-discrete quantum maps, i.e., Anderson map and the standard map. Further, the features of delocalized dynamics is discussed in comparison with a limit model which has no static disordered part.

cond-mat.dis-nn↗

arXiv2021

Presence and Absence of Delocalization-localization Transition in Coherently Perturbed Disordered Lattices

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 $d=3$.

cond-mat.dis-nn↗

arXiv2019

Critical Phenomena of Dynamical Delocalization in Quantum Maps:standard map and Anderson map

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 $t^α$~($t$:time) agrees well with the prediction of one-parameter scaling theory $α=2/(M+1)$, 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.

cond-mat.dis-nn↗

arXiv2019

Mean first passage times reconstruct the slowest relaxations in potential energy landscapes of nanoclusters

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.

physics.atm-clus↗

arXiv2018

Changes of graph structure of transition probability matrices indicate the slowest kinetic relaxations

Graphs of the most probable transitions for a transition probability matrix, $e^{τK}$, i.e., the time evolution matrix of the transition rate matrix $K$ over a finite time interval $τ$, are considered. We study how the graph structures of the most probable transitions change as functions of $τ$, thereby elucidating that a kinetic threshold $τ_g$ for the graph structures exists. Namely, for $τ<τ_g$, the number of connected graph components are constant. In contrast, for $τ\geq τ_g$, recombinations of most probable transitions over the connected graph components occur multiple times, which introduce drastic changes into the graph structures. Using an illustrative multi-funnel model, we show that the recombination patterns indicate the existence of the eigenvalues and eigenvectors of slowest relaxation modes quite precisely. We also devise an evaluation formula that enables us to correct the values of eigenvalues with high accuracy from the data of merging processes. We show that the graph-based method is valid for a wide range of kinetic systems with degenerate, as well as non-degenerate, relaxation rates.

cond-mat.dis-nn↗

arXiv2018

A Quantum Damper

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.

cond-mat.stat-mech↗

arXiv2018

Slowest kinetic modes revealed by metabasin renormalization

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.

cond-mat.mes-hall↗

arXiv2017

Scaling Properties of Dynamical Localization in Monochromatically Perturbed Quantum Maps: standard map and Anderson map

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.

cond-mat.dis-nn↗

arXiv2016

Measuring lifetime of correspondence with classical decay of correlation in quantum chaos

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.

cond-mat.stat-mech↗

arXiv2016

Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors

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.

cond-mat.stat-mech↗

arXiv2016

On the origin of atomistic mechanism of rapid diffusion in alkali halide nanoclusters

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.

cond-mat.mes-hall↗

arXiv2015

Critical Phenomena of Dynamical Delocalization in Quantum Anderson Map

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 $ε_c$ of the normalized perturbation at the transition point remarkably decreases as $ε_c \sim (M-1)^{-1}$.

cond-mat.dis-nn↗