arXiv subjects

Hiroaki S. Yamada

Publications and source records attributed to Hiroaki S. Yamada.

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

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↗

arXiv2018

Role of self-loop in cell-cycle network of budding yeast

Study of network dynamics is very active area in biological and social sciences. However, the relationship between the network structure and the attractors of the dynamics has not been fully understood yet. In this study, we numerically investigated the role of degenerate self-loops on the attractors and its basin size using the budding yeast cell-cycle network model. In the network, all self-loops negatively surpress the node (self-inhibition loops) and the attractors are only fixed points, i.e. point attractors. It is found that there is a simple division rule of the state space by removing the self-loops when the attractors consist only of point attractors. The point attractor with largest basin size is robust against the change of the self-inhibition loop. Furthermore, some limit cycles of period 2 appear as new attractor when a self-activation loop is added to the original network. It is also shown that even in that case, the point attractor with largest basin size is robust.

q-bio.MN↗

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

Localization of disordered harmonic chain with long-range correlation

In the previous paper [Yamada, Chaos, Solitons $\&$ Fractals, {\bf 109},99(2018)], we investigated localization properties of one-dimensional disordered electronic system with long-range correlation generated by modified Bernoulli (MB) map. In the present paper, we report localization properties of phonon in disordered harmonic chains generated by the MB map. Here we show that Lyapunov exponent becomes positive definite for almost all frequencies $ω$ except $ω=0$, and the $B-$dependence changes to exponential decrease for $B > 2 $, where $B$ is a correlation parameter of the MB map. The distribution of the Lyapunov exponent of the phonon amplitude has a slow convergence, different from that of uncorrelated disordered systems obeying a normal central-limit theorem. Moreover, we calculate the phonon dynamics in the MB chains. We show that the time-dependence of spread in the phonon amplitude and energy wave packet changes from that in the disordered chain to that in the periodic one, as the correlation parameter $B$ increases.

cond-mat.dis-nn↗

arXiv2017

Wavepacket Dynamics in One-Dimensional System with Long-Range Correlated Disorder

We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum $1/f^α$ ($α:$spectrum exponent) generated by Fourier filtering method. For relatively small $α<α_c(=2)$ time-dependence of mean square displacement (MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that $α-$dependence of the dynamical localization length (DLL) determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength $W$. Furthermore, scaled MSD by the DLL almost obeys an universal function from the ballistic to the localization regime in the various combinations of the parameters $α$ and $W$.

cond-mat.dis-nn↗

arXiv2017

Localization in One-Dimensional Tight-Binding Model with Chaotic Binary Sequences

We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition (SNCT). The energy sequences in question might be characterized by their correlation parameter $B$ and the potential strength $W$. The quantum states resulting from such sequences have been characterized in the two ways: Lyapunov exponent at band centre and the dynamics of the initially localized wavepacket. Specifically, the $B-$dependence of the relevant Lyapunov exponent's decay is changing from linear to exponential one around the SNCT ($B \simeq 2$). Moreover, here we show that even in the nonstationary regime, mean square displacement (MSD) of the wavepacket is noticeably suppressed in the long-time limit (dynamical localization). The $B-$dependence of the dynamical localization lengths determined by the MSD exhibits a clear change in the functional behaviour around SNCT, and its rapid increase gets much more moderate one for $B \geq 2$. Moreover we show that the localization dynamics for $B>3/2$ deviates from the one-parameter scaling of the localization in the transient region.

cond-mat.dis-nn↗

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

Delocalization in One-Dimensional Tight-Binding Models with Fractal Disorder II: Existence of Mobility Edge

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88, 264]. In the present work, we study the energy ($E \neq 0$) dependence of the normalized localization length and the delocalization of the wavefunction at the different energy in the same system. The mobility edges in the LDT arise when the fractal dimension of the potential landscape is larger than the critical value depending on the disorder strength, which is consistent with the previous result.In addition, we present the distribution of individual NLL and Lyapunov exponent in the system with LDT.

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↗

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↗