Critical phenomena of dynamical delocalization in a quantum Anderson map

Yamada, Hiroaki; Matsui, Fumihiro; Ikeda, Kensuke S.

doi:10.1103/physreve.92.062908

Cited by 8 publications

(10 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 10(b) also implies that D(T ) is controlled by ǫ/ 2 , as is the case of the localization length of Eq. (12). Thus the quantum regime we introduced without definition previously should be…”

Section: Diffusion Characteristicsmentioning

confidence: 99%

Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map

Yamada¹,

Matsui

Ikeda

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Diffusion Characteristicsmentioning

confidence: 99%

Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map

Yamada¹,

Matsui

Ikeda

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…The breaking of the dynamical localization in a single quantum kicked rotor via a modulation of the kick amplitude has already been considered. Examples are a modulation via d − 1 incommensurate frequencies [87][88][89][90][91] which induces Anderson localization/delocalization transition and a kick with modulated amplitude which undergoes decoherence and quantum-to-classical transition [92][93][94]. In all the cases, the properties of the modulation are crucial in determining the response of the system, especially if the modulation is noisy [95][96][97][98][99]142].…”

Section: Introductionmentioning

confidence: 99%

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

et al. 2018

View full text Add to dashboard Cite

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

show abstract

“…It is also feasible to experimentally realize the dynamical localization transition through the diffusion of wave packets in the pulsed 1D incommensurate optical lattice such as the KHM. [33] On the other hand, we also investigated the characteristics of the LDT in the polychromatically perturbed kicked Anderson model (KAM), and the results that correspond well with those in the KR have been obtained [34][35][36][37][38][39]. Note that in our previous paper, we used the expression Anderson map (AM) for the kicked Anderson model (KAM).…”

Section: Introductionmentioning

confidence: 92%

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

Yamada¹,

Ikeda²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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 quasiperiodic perturbation composed of M −modes. Both models are localized in the monochromatically perturbed case M = 1. KHM shows localization-delocalization transition (LDT) above M ≥ 2 as increase of the perturbation strength ǫ. 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 ≥ 3. In addition, we investigate the diffusive property of the delocalized wave packet for ǫ above the critical strength ǫc (ǫ > ǫc). We also introduce other type systems without localization, which takes place a ballistic to diffusive transition in the wave packet dynamics as the increase of ǫ. In both systems, the ǫ−dependence of the diffusion coefficient well coincide with that in the other type system for large ǫ(> 1).

show abstract

Critical phenomena of dynamical delocalization in a quantum Anderson map

Cited by 8 publications

References 35 publications

Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map

Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

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

Contact Info

Product

Resources

About