Localization length versus level repulsion in one-dimensional driven disordered quantum wires

Benito-Matías, E.; Molina, Rafael A.

doi:10.1103/physrevb.96.174202

Cited by 8 publications

(4 citation statements)

References 57 publications

(73 reference statements)

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“…We also note related studies of non-interacting driven systems. In particular, we flag studies of tight-binding models which examine the effect of periodically driving a disordered one-dimensional system on localization length [35][36][37] , conductance 38,39 , spectral statistics 40 , and localization properties of Floquet operator eigenstates 41 . Ref 41 also studied dissipative non-linear charge response (but not heating) of Anderson insulators, but they worked primarily in the strong drive limit E 0 ω.…”

Section: Introductionmentioning

confidence: 99%

Mott, Floquet, and the response of periodically driven Anderson insulators

et al. 2018

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We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times-which is the physics of Floquet late time statesand strong electric fields. This results in a "phase diagram" in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by preexisting Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.

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Section: Introductionmentioning

confidence: 99%

Mott, Floquet, and the response of periodically driven Anderson insulators

et al. 2018

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“…length: In the previous section, we noticed that the spectral properties of β-ensemble and RPE have an important difference: clustering transition occurs at γ ET for β-ensemble and γAT for RPE. The degree of level repulsion, β been interpreted localization length in systems [75][76][77][78] though there are exceptions as well [79]. Now we look at the entropic localization length w.r.t.…”

Section: Properties Of Energy Statesmentioning

confidence: 99%

Non-ergodic extended states in $β$-ensemble

Das,

Ghosh

2021

Preprint

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Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the βensemble, known for its structural simplicity. However, eigenvector properties of β-ensemble remain largely unexplored, despite energy level correlations being thoroughly studied. In this work we numerically study the eigenvector properties of β-ensemble and identify the ergodic transition point (γET = 0) and localization transition point (γAT = 1) where we express the repulsion parameter as β = N −γ . Thus other than Rosenzweig-Porter ensemble (RPE), β-ensemble is another example where Non-Ergodic Extended (NEE) states are observed over a finite interval of parameter values (0 < γ < 1). We find that the chaotic-integrable transition coincides with the ergodic transition unlike the RPE or the 1-D disordered spin-1/2 Heisenberg model where this coincidence occurs at the localization transition. As a result, the dynamical time-scales in the NEE regime of β-ensemble behave differently than the former models.

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“…Statistical analysis of spectra is a very important tool for understanding the dynamics of quantum and wave systems [1][2][3]. Quantifying the level repulsion, for example, it is possible to study the transition between integrable and chaotic quantum or wave systems [4][5][6][7][8][9][10][11][12][13][14], between localized and extended states in disordered systems [15][16][17][18] and between ergodic and many-body localized phases in many body strongly correlated systems [19][20][21][22][23]. This relationship is based on the identification of complex wave or quantum spectra with random matrix theory (RMT) [24].…”

Section: Introductionmentioning

confidence: 99%

Missing levels in intermediate spectra

Hita-Pérez,

Muñoz,

Molina

2023

J. Phys. A: Math. Theor.

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We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The expression is based on the Brody distribution, the most widely used for fitting mixed spectra as a function of one parameter.By using Monte Carlo simulations of intermediate spectra based on the $\beta$-Hermite ensemble of Random Matrix Theory, we evaluate the quality of the formulaand its suitability for fitting purposes.Estimations of the Brody parameter and the fraction of missing levelscan be obtained by a least-square two-parameter fitting of the experimental $P(s)$. The results should be important to distinguish the origins of deviations from RMT in experimental spectra.

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Localization length versus level repulsion in one-dimensional driven disordered quantum wires

Cited by 8 publications

References 57 publications

Mott, Floquet, and the response of periodically driven Anderson insulators

Mott, Floquet, and the response of periodically driven Anderson insulators

Non-ergodic extended states in $β$-ensemble

Missing levels in intermediate spectra

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