Spectral Renormalization Research Articles

Applications of spectral renormalization method to the research of nonlocal optical spatial soliton

We use spectral renormalization method to solve the nonlocal nonlinear Schrdinger equation, which gives accurate waveform of nonlocal optical spatial soliton. The relation between critical power and critical beamwidth is acquired in different nonlocal conditions. We discovered that optical spatial soliton exists stably in any nonlocal degree. Comparing analytic solution with numerical solution for different response functions, we find that they are consistent only under strong nonlocal and weak nonlocal conditions. The effective range of analytic solution is also given.

Singular Solutions of the Biharmonic Nonlinear Schrödinger Equation

We consider singular solutions of the $L^2$-critical biharmonic nonlinear Schrödinger equation. We prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of $L^2$-norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of a ground-state solution. We use asymptotic analysis to show that the blowup rate of peak-type singular solutions is slightly faster than that of a quartic-root, and the self-similar profile is given by the ground-state standing wave. These findings are verified numerically (up to focusing levels of $10^8$) using an adaptive grid method. We also use the spectral renormalization method to compute the ground state of the standing-wave equation, and the critical power for collapse, in one, two, and three dimensions.

Solitons and spectral renormalization methods in nonlinear optics

Localized wave solutions, often referred to as solitary waves or solitons, are important classes of solutions in nonlinear optics. In optical communications, weakly nonlinear, quasi-monochromatic waves satisfy the “classical” and the “dispersion-managed” nonlocal nonlinear Schrodinger equations, both of which have localized pulses as special solutions. Recent research has shown that mode-locked lasers are also described by similar equations. These systems are variants of the classical nonlinear Schrodinger equation, appropriately modified to include terms which model gain, loss and spectral filtering that are present in the laser cavity. To study their remarkable properties, a computational method is introduced to find localized waves in nonlinear optical systems governed by these equations.

Dark and gray spatial optical solitons in Kerr-type nonlocal media

With the spectral renormalization method (the Fourier iteration method) we compute dark/gray soliton solutions in Kerr-type nonlocal media and find it agrees well with the analytical results. It is indicated when the characteristic nonlocal length is less than a certain critical value, the gray soliton's maximal transverse velocity does not vary with the characteristic nonlocal length, otherwise such maximal velocity decreases with the characteristic nonlocal length.

Ground State and Resonances in the Standard Model of the Non-Relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.

Double scale analysis of a Schrödinger–Poisson system with quantum wells and macroscopic nonlinearities in dimension 2 and 3

We consider the stationary Schrodinger-Poisson model with a background potential describing a quantum well. The Hamiltonian of this system composes of contributions the background potential well plus a nonlinear repulsive term which extends on different length scales with ratio parametrized by the small parameter h. With a partition function which forces the particles to remain in the quantum well, the limit h?0 in the nonlinear system leads to different asymptotic behaviours, including spectral renormalization, depending on the dimensions 1, 2 or 3.

An indirect probe of the possible half-metallic nature of LiFePO4 using resonant inelastic X-ray scattering

Abstract The Fe site in LiFePO 4 was probed resonantly and non-resonantly at the L 2,3 edge. A suspected half-metal, the experimental results were compared to band structure calculations to understand the electronic structure. We found that the probability of promoting an electron to the unoccupied band through simple photoexcitation or through scattering is highly influenced by magnon–exciton coupling. We have also found evidence that the correlation self-energy has a momentum-dependant component, causing spectral renormalization of the Fe 3d PDOS. Our experimental results are consistent with the predicted band, structure of LiFePO 4 .

Spectral renormalization method for computing self-localized solutions to nonlinear systems

A new numerical scheme for computing self-localized states--or solitons--of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.

THEORY OF OPTICAL ABSORPTION IN HIGH-TEMPERATURE SUPERCONDUCTORS

We review the optical absorption spectrum of a high-temperature superconductor and present a simple theory which explains it in some detail. An experiment is proposed to determine the averaged spectral density and wave function renormalization functions of the charge carriers in the normal and in the superconducting states. This might help measure the superconducting gap.

Investigation of the temperature dependence of electron and phonon Raman scattering in single crystal YBa2Cu3O6.952

Detailed Raman-scattering measurements have been performed on high-quality YBa2Cu3O6.952 single crystal (Tc=93 K, ΔTc=0.3 K). A sharp (FWHM 7.2 cm−1 at 70 K and 10.0 cm−1 at 110 K) 340 cm−1phonon mode has been observed inB1g polarization. An electronic scattering peak at 500 cm−1 in theB1g polarization extends down to 250 cm−1. These FWHM values determine the upper limit of the homogeneous linewidth of the phonon and electronic excitations. The start of the electronic spectral function renormalization and of the 340 cm−1 mode anomalies (frequency softening, linewidth sharpening, and intensity increase) have been observed to occur approximately 40 K aboveTc. The 340 cm−1 mode Fano shape analysis has been performed and the temperature dependences of the Fano shape parameters have been estimated. All 340 cm−1 mode anomalies have been explained by the electronic spectral function renormalization.