arXiv subjects

Joshua D. Bodyfelt

Publications and source records attributed to Joshua D. Bodyfelt.

14 recordsLinked to original sources

arXiv2018

Nonlinear dynamic interpretation of quantum spin

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body, anti-ferromagnetic ordering, highly coupled quantum spin and a semi-classical interpretation of the torque on a spin magnetic moment in the presence of a magnetic field. The deterministic nonlinear differential coupling equation is used to introduce chaos, which is necessary to reproduce the correct statistical quantum results.

quant-ph↗

arXiv2018

Nonlinear Semi-Classical 3D Quantum Spin

In an effort to provide an alternative method to represent a quantum spin, a precise 3D nonlinear dynamics method is used. A two-sided torque function is created to mimic the unique behavior of the quantum spin. A full 3D representation of the magnetic field of a Stern-Gerlach device was used as in the original experiment. Furthermore, the temporarily driven nonlinear damped model exhibits chaos, but struggles to be consistent through azimuthal angles in reproducing the quantum spin statistics.

quant-ph↗

arXiv2017

Localization of weakly disordered flat band states

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths $ξ$ that diverge with a variety of unconventional exponents $ν$, $ξ\sim 1/W^ν$.

cond-mat.dis-nn↗

arXiv2015

Flatband Engineering of Mobility Edges

Properly modulated flatband lattices have a divergent density of states at the flatband energy. Quasiperiodic modulations are known to host a metal insulator transition already in one space dimension. Their embedding into flatband geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flatband lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.

cond-mat.str-el↗

arXiv2014

Flat Bands Under Correlated Perturbations

Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $ξ\sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions.

cond-mat.dis-nn↗

arXiv2014

Detangling Flat Bands into Fano Lattices

Macroscopically degenerate flat bands (FB) in periodic lattices host compact localized states which appear due to destructive interference and local symmetry. Interference provides a deep connection between the existence of flat band states (FBS) and the appearance of Fano resonances for wave propagation. We introduce generic transformations detangling FBS and dispersive states into lattices of Fano defects. Inverting the transformation, we generate a continuum of FB models. Our procedure allows us to systematically treat perturbations such as disorder and explain the emergence of energy-dependent localization length scaling in terms of Fano resonances.

cond-mat.mes-hall↗

arXiv2013

High Order Three Part Split Symplectic Integration Schemes

Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for a few special cases. In this work, we present and compare different ways to construct high order symplectic schemes for general Hamiltonian systems that can be split in three integrable parts. We use these techniques to numerically solve the equations of motion for a simple toy model, as well as the disordered discrete nonlinear Schrödinger equation. We thereby compare the efficiency of symplectic and non-symplectic integration methods. Our results show that the new symplectic schemes are superior to the other tested methods, with respect to both long term energy conservation and computational time requirements.

nlin.CD↗

arXiv2013

Scaling Theory of Heat Transport in Quasi-1D Disordered Harmonic Chains

We introduce a variant of the Banded Random Matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting beta-function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction, based on the powerful ideas of scaling theory.

cond-mat.dis-nn↗

arXiv2013

Enhanced Transmission and Giant Faraday Effect in Magnetic Metal-Dielectric Photonic Structures

Due to their large electric conductivity, stand-alone metallic films are highly reflective at microwave frequencies. For this reason, it is nearly impossible to observe Faraday rotation in ferromagnetic metal layers, even in films just tens of nanometers thick. Here, we show using numerical simulations that a stack of cobalt nano-layers interlaced between dielectric layers can become highly transmissive and display a large Faraday rotation in a finite frequency band. A 45-degree Faraday rotation can be achieved with metallic ferromagnetic layers as thin as tens of nanometers.

physics.optics↗

arXiv2012

Subdiffusion of nonlinear waves in quasiperiodic potentials

We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for interacting atomic condensates [Phys. Rev. Lett. 106, 230403 (2011)]. We extend the analysis of the characteristics of the subdiffusive dynamics to large temporal and spatial scales. Our results for the second moment $m_2$ consistently reveal an asymptotic $m_2 \sim t^{1/3}$ and intermediate $m_2 \sim t^{1/2}$ laws. At variance to purely random systems [Europhys. Lett. 91, 30001 (2010)] the fractal gap structure of the linear wave spectrum strongly favors intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments.

cond-mat.dis-nn↗

arXiv2012

Influence of boundary conditions on quantum escape

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important - moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

quant-ph↗

arXiv2010

One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems

We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to investigate the interplay of Anderson localization and nonlinearity based on the powerful ideas of scaling theory.

cond-mat.dis-nn↗

arXiv2009

Probing Localization in Absorbing Systems via Loschmidt Echos

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi one-dimensional microwave cavity filled with randomly distributed scatterers.

cond-mat.dis-nn↗

arXiv2007

Scaling properties of delay times in one-dimensional random media

The scaling properties of the inverse moments of Wigner delay times are investigated in finite one-dimensional (1D) random media with one channel attached to the boundary of the sample. We find that they follow a simple scaling law which is independent of the microscopic details of the random potential. Our theoretical considerations are confirmed numerically for systems as diverse as 1D disordered wires and optical lattices to microwave waveguides with correlated scatterers.

cond-mat.dis-nn↗