Numerical study of anomalous diffusion of light in semicrystalline polymer structures

Kostadinova, Eva; Padgett, Joshua Lee; Liaw, Constanze; Matthews, L. S.; Hyde, Truell

doi:10.1103/physrevresearch.2.043375

Cited by 8 publications

(4 citation statements)

References 76 publications

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“…Weak localization and strong Anderson localization have been conjectured and subsequently observed in experiments [6][7][8][9][10]. As a wave phenomenon, Anderson localization has been demonstrated for electrons [11][12][13][14][15][16], sound [17], photons [18][19][20][21][22][23][24][25], and ultra cold atoms [26].…”

Section: Introductionmentioning

confidence: 87%

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

et al. 2021

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We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

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Section: Introductionmentioning

confidence: 87%

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

et al. 2021

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“…Some general remarks on the IM: the goal is to calculate average quantities, such as the average Green's function or the average product of two Green's functions, with respect to the random matrix elements of the Hamiltonian Ĥ [21]. This should be seen as an alternative to studies, where the distribution of the random Hamiltonian and its spectrum is considered [23][24][25]. Average quantities are sufficient to discuss many physically motivated questions, such as transport [18,22].…”

Section: Model: Immentioning

confidence: 99%

Localization by particle–hole symmetry breaking: a loop expansion

Ziegler¹

2022

J. Phys. A: Math. Theor.

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Localization by a broken particle-hole symmetry in a random system of non-interacting quantum particles is studied on a $d$--dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure, where the latter is described by a Grassmann functional integral. Within a loop expansion we find for small loops diffusion in the case of particle-hole symmetry. Breaking the particle-hole symmetry results in the creation of random dimers, which suppress diffusion and lead to localization on the scale $\sqrt{D/|\mu|}$, where $D$ is the effective diffusion coefficient at particle-hole symmetry and $\mu$ is the parameter related to particle-hole symmetry breaking.

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“…The authors have previously applied the spectral approach to the study of transport in disordered 1D, 2D, and 3D lattices [59]- [62], [88], [89], where the amount of stochastic disorder 𝑐 was varied in the potential energy term of the examined Hamiltonian. The recently developed Fractional Laplacian Spectral (FLS) method [50], [77] applies the spectral approach to a Hamiltonian with random disorder in potential energy term and a kinetic energy term represented by the discrete fractional Laplacian, which allows for modeling disordered media with nonlocal interactions.…”

Section: Energy Transport a Fractional Laplacian Spectral (Fls) Approachmentioning

confidence: 99%

Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer

et al. 2021

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This work presents a theoretical investigation of active turbulence in a dusty plasma monolayer, where energy is injected at the individual particle level and transported to larger scales, leading to the spontaneous formation of spatially disordered flow patterns. Many-body simulations of 10,000-particle dusty plasma monolayers are used to demonstrate how the global dynamics depend on the statistical properties of the dust assembly for realistic laboratory conditions. We find that spatial defects due to variations in the dust size distribution and charge-driven nonlocal interactions resulting in anomalous dust diffusion, are key factors for the onset of instabilities. The resulting dynamics exhibits features of inertial turbulence over slightly less than one decade of scales, down to scales on the order of the particle diameter. These processes are examined analytically using a recently developed Fractional Laplacian Spectral (FLS) technique, which identifies the active energy channels as a function of scale, disorder concentration, and nonlocality. The predictions from the theoretical (spectral) analysis demonstrate agreement with the results from the many-body (kinetic) simulations, thus providing a powerful tool for the study of active turbulence.

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Numerical study of anomalous diffusion of light in semicrystalline polymer structures

Cited by 8 publications

References 76 publications

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Localization by particle–hole symmetry breaking: a loop expansion

Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer

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