Transport through quasi-one-dimensional wires with correlated disorder

Herrera-González, I. F.; Ja, Méndez-Bermúdez; Fm, Izrailev

doi:10.1103/physreve.90.042115

Cited by 9 publications

(6 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, in tight-binding systems, the on-site term

represents losses (

) and gain (

). Moreover, the term

allows adding losses and gain to tight-binding systems locally by adding this term to selected sites (in regular arrays, the addition of the term

to border sites is commonly used to study scattering and transport properties; see, e.g., [ 24 , 25 , 26 ]), globally by adding this term to all sites in the system (in linear chains, the addition of the term

to all sites has been used to represent a system coupled to a common decay channel; see, e.g., [ 27 , 28 ]), and in a balanced way by adding

to all sites with the same proportion of plus and minus signs (the addition of alternating

and

terms to the sites of one-dimensional non-disordered arrays produces

-symmetric wires; see, e.g., [ 29 , 30 ]). In our model, we choose the latter setup, where balanced implies that the network is formed by an even number of vertices.…”

Section: Introductionmentioning

confidence: 99%

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Martinez-Martinez

Méndez-Bermúdez

2019

Entropy

View full text Add to dashboard Cite

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivity α , and the losses-and-gain strength γ . Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i γ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ ≡ ξ ( N , α , γ ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ < 0.1 ( 10 < ξ ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1 < ξ < 10 . Moreover, to extend the applicability of our findings, we demonstrate that for fixed ξ , the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.

show abstract

“…Indeed, in tight-binding systems, the on-site term

represents losses (

) and gain (

). Moreover, the term

allows adding losses and gain to tight-binding systems locally by adding this term to selected sites (in regular arrays, the addition of the term

to all sites has been used to represent a system coupled to a common decay channel; see, e.g., [ 27 , 28 ]), and in a balanced way by adding

to all sites with the same proportion of plus and minus signs (the addition of alternating

and

terms to the sites of one-dimensional non-disordered arrays produces

-symmetric wires; see, e.g., [ 29 , 30 ]). In our model, we choose the latter setup, where balanced implies that the network is formed by an even number of vertices.…”

Section: Introductionmentioning

confidence: 99%

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Martinez-Martinez

Méndez-Bermúdez

2019

Entropy

View full text Add to dashboard Cite

show abstract

“…Single-particle Anderson localization in quasi-1D geometries with correlated disorder is already a challenging problem [1][2][3][4]. With interactions, the situation becomes even more interesting.…”

Section: Setting Objectives and Scopementioning

confidence: 99%

Anderson localization of Bogoliubov excitations on quasi‐1D strips

2015

View full text Add to dashboard Cite

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths. I. SETTING, OBJECTIVES, AND SCOPESingle-particle Anderson localization in quasi-1D geometries with correlated disorder is already a challenging problem [1][2][3][4]. With interactions, the situation becomes even more interesting. Here, we study the localization properties of the Bogoliubov quasi-particles (BQP) of weakly disordered Bose gases at zero temperature on quasi-1D lattices. While interactions tend to screen the disorder and thus stabilize extended (quasi-)condensates [5] for weak disorder [6,7], BQPs are expected to be localized irrespective of their energy or disorder strength in low dimensions [8][9][10], thus emulating noninteracting particles in the orthogonal Wigner-Dyson universality class [11]. Yet, BQPs differ qualitatively from noninteracting particles because of their collective, phononlike behavior at low energy. Moreover, they experience a randomness mediated by the inhomogeneous condensate background, which responds nonlinearly and nonlocally to the bare disorder [12][13][14]. This interplay has been extensively examined in 1D [15][16][17][18], where direct backscattering provides the only pathway to localization.In this Letter, we discuss the localization length of BQPs on quasi-1D planar lattices of transverse width N × 1 (shown in Fig. 1a). While the techniques developed below also apply to N x ×N y bars, strips provide the simplest realization of a multi-channel geometry, where phase-coherent scattering between modes is the rule. The bosons are described by the Bose-Hubbard (BH) model with on-site interaction U > 0, hopping t (with periodic boundary conditions across the strip) and on-site disorder V x . The random potential V x is drawn from a Gaussian distribution and has no spatial correlation on the lattice scale, V x V x = δ xx V 2 , where the bar denotes disorder averaging and V 2 is the on-site variance. For each realization of disorder, the mean-field (MF) ground-state density n x is determined by the condensate amplitude Φ x = √ n x that solves the discrete Gross-Pitaevskii (GP)where the sum runs over the nearest neighbors of x. The chemical potential µ controls the average occupation n = n x . In the limit of large occupations [19], an expansion of the BH Hamiltonian around the MF solution yields the Bogoliubov-de Gennes (BdG) equationswhere u x and v x are the BQP particle and hole components at energy E. These Bogoliubov excitations determine ground-state properties as well as the (thermo-) dynamical response of the system. In the remainder of this paper, we compute the dependence of the BQP localization length on the excitation energy. We first present a numerical transfer-m...

show abstract

“…The quantum diffusion in 1D tight-binding model has an enriched background [1][2][3][4] . First, a numerical evidence was constructed by L. Hufnagel et al [5] supporting that the variance of a wave packet in 1D tight-binding can show a superballistic increase (σ 2 = t ν with 2 < ν 3) for parametrically large time intervals with the appropriate model.…”

Section: Introductionmentioning

confidence: 99%

Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

Gholami

Lashkami

2017

Phys. Rev. E

View full text Add to dashboard Cite

As an unusual type of anomalous diffusion behavior, namely (transient) superballistic transport, has been experimentally observed recently, but it is not yet well understood. In this paper, we investigate the white noise effect (in the Markov approximation) on quantum diffusion in one-dimensional tight-binding models with a periodic, disordered, and quasiperiodic region of size L attached to two perfect lattices at both ends in which the wave packet is initially located at the center of the sublattice. We find that in a completely localized system, inducing noise could delocalize the system to a desirable diffusion phase. This controllable system may be used to investigate the interplay of disorder and white noise, as well as to explore an exotic quantum phase.

show abstract

Transport through quasi-one-dimensional wires with correlated disorder

Cited by 9 publications

References 61 publications

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Anderson localization of Bogoliubov excitations on quasi‐1D strips

Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

Contact Info

Product

Resources

About