Localization in a disordered elastic medium near two dimensions

John, Sajeev; Sompolinsky, Haim; Stephen, Michael J.

doi:10.1103/physrevb.27.5592

Cited by 271 publications

(226 citation statements)

References 10 publications

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“…The mobility edge, defined by D 0, obeys an IoffeRegel-type criterion as derived microscopically by John et al [18] and Economou et al [19], and agrees with the numerical studies of the Anderson tight binding model [20,21]. The cutoff removes short wave paths from the return probability and influences the exact location of the mobility edge [19,22].…”

Section: (Received 10 January 2000)supporting

confidence: 55%

Reflection and Transmission of Waves near the Localization Threshold

2000

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Section: (Received 10 January 2000)supporting

confidence: 55%

Reflection and Transmission of Waves near the Localization Threshold

2000

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“…Treating δJ k as a perturbation, it is easy to find the localization length following Refs. [20,21]. Indeed, the mean free time can be found by the Fermi golden rule, to go as τ −1 ∼ ω 2 , while the mean free path goes as √ J 0 U 0 τ .…”

Section: (14) Thenmentioning

confidence: 99%

Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

2008

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We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as (ω) ∼ 1/ω α . We show that the well known result α = 2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, α starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, α = 1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays. One of the most challenging problems of quantum many body physics is the behavior of stongly interacting matter in a disordered environment. In this paper we investigate the universal properties of superfluids in such systems, near the superfluid insulator transition. Interest in this problem arises in many independent contexts, in work on granular superconducting films and wires [1, 2,3], Helium condensates in vycor [4], and recent experiments on Bose condensates in optical traps. In particular, issues such as the expansion of a noninteracting Bose condensate through a random potential [5], excitations in an interacting Bose Einstein condensate in a random potential [6,7], and the possibility of the observation of the Bose glass phase [8,9] were explored in very recent theoretical and experimental papers. As important is the possibility of investigating the behavior of disordered superconductors in a controlled fashion using Josephson junction arrays, as in Refs. [10,11,12]. In low dimensional quantum systems, where symmetry broken phases are very fragile, we expect the most dramatic manifestations of the interplay of disorder and interactions. The existence of the Bose-glass phase was established in Refs. [13,14], where the scaling and renormalization group (RG) picture of the 1d superfluid-insulator transition at weak disorder was also established. Recently, much theoretical progress was afforded through real-space RG approaches in the case of dissipative [15] and closed [16,17] bosonic chains, where the properties of the SF-insulator transition at strong disorder were established.In this paper, we study the excitations of the superfluid phase in a bosonic chain with a strongly random potential and interactions, near the SF-insulator transition. Capitalizing on the real-space RG understanding of this transition [16,17], we analyze the localization length of phonons (i.e., Bogoliubov quasiparticles) as a function of their frequency and wave number. Deep in the superfluid phase, when the random potential is weak, the phonon localization length (ω) at small ω diverges as [6,18,19]

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“…21 Above the IR crossover frequency, the phonon might become nonpropagating and/or localized. [24][25][26] Therefore, it is reasonable to expect negligible phonon interference effects for phonon frequency much greater than 1.4 THz. Below 1.4 THz, however, the MFP of phonons in aSiO 2 increases very fast to values over 10 nm as phonon frequency reduces.…”

Section: Introductionmentioning

confidence: 99%

Phonon interference in crystalline and amorphous confined nanoscopic films

Liang

Wilson

Keblinski

2017

Journal of Applied Physics

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Using molecular dynamics phonon wave packet simulations, we study phonon transmission across hexagonal (h)-BN and amorphous silica (a-SiO 2 ) nanoscopic thin films sandwiched by two crystalline leads. Due to the phonon interference effect, the frequency-dependent phonon transmission coefficient in the case of the crystalline film (Sijh-BNjAl heterostructure) exhibits a strongly oscillatory behavior. In the case of the amorphous film (Sija-SiO 2 jAl and Sija-SiO 2 jSi heterostructures), in spite of structural disorder, the phonon transmission coefficient also exhibits oscillatory behavior at low frequencies (up to $1.2 THz), with a period of oscillation consistent with the prediction from the two-beam interference equation. Above 1.2 THz, however, the phonon interference effect is greatly weakened by the diffuse scattering of higher-frequency phonons within an a-SiO 2 thin film and at the two interfaces confining the a-SiO 2 thin film. Published by AIP Publishing.

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Localization in a disordered elastic medium near two dimensions

Cited by 271 publications

References 10 publications

Reflection and Transmission of Waves near the Localization Threshold

Reflection and Transmission of Waves near the Localization Threshold

Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

Phonon interference in crystalline and amorphous confined nanoscopic films

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