Quasiresonant diffusion of wave packets in one-dimensional disordered mosaic lattices

Nguyen, Ba Phi; Phung, Duy Khuong; Kim, Kihong

doi:10.1103/physrevb.106.134204

Cited by 3 publications

(7 citation statements)

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“…Although the resonance energies have been correctly derived, there has been a mischaracterization regarding the nature of the resonant states, incorrectly labeling them as entirely extended states. In both this paper and our previous work [44], we provide unambiguous evidence through calculations of various physical quantities that these states are not entirely extended; rather, they exhibit power-law localized critical behavior. de Moura et al investigated the dynamics of a wave packet launched in a diluted Anderson lattice and observed a subdiffusive spreading characterized by the mean square displacement behavior ⟨m 2 (t)⟩ ∝ t 0.5 [53].…”

Section: Introductionsupporting

confidence: 60%

“…We derived a simple analytical formula for these energies, which interestingly takes the same form as the resonance energy formula found in the binary random N-mer model [42]. However, it is important to note that this similarity is purely coincidental, as the underlying mechanisms are entirely distinct [44]. The binary random N-mer model exhibits superdiffusive wave packet spreading and completely extended states at resonance energies.…”

Section: Introductionmentioning

confidence: 68%

“…At all the other sites, the on-site potential remains constant with a value of V 0 . The disordered mosaic lattice model has been the subject of recent investigation, with emphasis on numerical analysis of the time-dependent reflectance of wave packets incident upon a lattice with a large length L [44]. The current study significantly expands on previous research by exploring additional aspects of the transport and localization properties of the same model, within the context of both stationary and non-stationary problems.…”

Section: Modelmentioning

confidence: 95%

“…L = 3000), we find that T remains non-negligible only at the (κ − 1) special energy values, such as E = 0 for κ = 2, E = ±1 for κ = 3, and E = 0, ± √ 2 for κ = 4, as shown in figures 2(g)-(i). At these energies, the transmittance decays much more slowly than at other values of E where it decays exponentially with L. Recently, we have investigated the characteristics of these spectral points, primarily by analyzing the timedependent reflectance of the incident wave packet through numerical calculations [44]. We have demonstrated that in the long-time limit, almost all the incident wave packets exhibit the exponential localization behavior, whereas those at a discrete set of the (κ − 1) energy values given by…”

Section: Wave Transmittancementioning

confidence: 99%

“…Our recent numerical investigation explored the time-dependent reflection of wave packets incident on an effectively semi-infinite disordered mosaic lattice chain, where disordered onsite potentials are inserted into the lattice only at equally spaced sites [44]. Through extensive numerical calculations, we discovered a discrete set of quasiresonance energies that deviate sharply from the ordinary Anderson localization behavior.…”

Section: Introductionmentioning

confidence: 99%

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Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations

Nguyen,

Kim

2023

J. Phys. A: Math. Theor.

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We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period $\kappa$ and the disorder strength $W$. We calculate the disorder averages $\langle T\rangle$, $\langle \ln T\rangle$, and $\langle P\rangle$, where $T$ is the transmittance and $P$ is the participation ratio, as a function ofenergy $E$ and system size $L$, for different values of $\kappa$ and $W$. For excitations at quasiresonance energies determined by $\kappa$, we find power-law scaling behaviors of the form $\langle T \rangle \propto L^{-\gamma_{a}}$,$\langle \ln T \rangle \approx -\gamma_g \ln L$, and $\langle P \rangle \propto L^{\beta}$, as $L$ increases to a large value.In the strong disorder limit, the exponents are seen to saturate at the values $\gamma_a \sim 0.5$, $\gamma_g \sim 1$, and $\beta\sim 0.3$,regardless of the quasiresonance energy value. This behavior is in contrast to the exponentiallocalization behavior occurring at all other energies.The appearance of sharp peaks in the participation ratio spectrum at quasiresonance energies provides additional evidence for the existence of an anomalous power-law localization phenomenon.The corresponding eigenstates demonstrate multifractal behavior and exhibit unique node structures.In addition, we investigate the time-dependent wave packet dynamics and calculate the mean square displacement $\langle m^2(t) \rangle$, spatial probability distribution, participation number, and return probability.When the wave packet's initial momentum satisfies the quasiresonance condition, weobserve a subdiffusive spreading of the wave packet, characterized by $\langle m^2(t) \rangle\propto t^{\eta}$ where $\eta$ is always less than 1.We also note the occurrence of partial localization at quasiresonance energies, as indicated by the saturation of the participation number and a nonzero value for the return probability at long times.

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Section: Introductionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 68%

Section: Modelmentioning

confidence: 95%

Section: Wave Transmittancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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