Search results for "transfer matrix"

Universality classes for wetting in two-dimensional random-bond systems

1991

Interface-unbinding transitions, such as those arising in wetting phenomena, are studied in two-dimensional systems with quenched random impurities and general interactions. Three distinct universality classes or scaling regimes are investigated using scaling arguments and extensive transfer-matrix calculations. Both the critical exponents and the critical amplitudes are determined for the weak- and the strong-fluctuation regime. In the borderline case of the intermediate-fluctuation regime, the asymptotic regime is not accessible to numerical simulations. We also find strong evidence for a nontrivial delocalization transition of an interface that is pinned to a line of defects.

Study of periodic Dielectric Frequency-Selective Surfaces under 3D plane wave incidence

2016

A periodic Dielectric Frequency-Selective Surface (DFSS) is studied under 3D plane-wave incidence, whose unit cell in the periodic direction is composed of a dielectric grating and a homogeneous dielectric layer. The structure is excited by a linearly polarized plane-wave. The procedure for computing the Brillouin diagram of the structure under 2D plane-wave incidence with TE or TM polarization was already described by the authors, and the extension to the 3D incidence case has been performed in a similar way. Following the same formalism, it has been obtained the Generalized Scattering Matrix (GSM) of one period of the infinite periodic lattice. This requires the knowledge of the modal spe…

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

2004

Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spati…

Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions

2013

We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

2014

28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…

Quantum wire with periodic serial structure

1991

Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schr\"odinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Casta\~no, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stu…

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…

The effect of disorder on optical spectra of conjugated polymers

1993

Abstract Using the semi-empirical parametrization of the Pariser-Parr-Pople model we determine the excitonic states in conjugated polymers. The employed parameters correspond to a moderate strength of the long-range Coulomb interaction. In order to take the disorder into account, the nearest-neighbour transfer matrix elements are chosen according to a random distribution. Averaging the results over a large number of chains of 100 sites, which are known to be sufficiently long so that finite-size effects become negligible, we obtain the linear and third-order nonlinear optical susceptibilities. With increasing disorder the linear absorption, the two-photon absorption and the third-harmonic g…

Generalized curved beam on elastic foundation solved by Transfer Matrix Method

2011

A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and tor…

Analysis of FBG reflection spectra under uniform and non-uniform transverse loads

2019

Loads applied transversely on the external surface of waveguides change their circular cross-sectional geometry generating birefringence. Due to this effect the reflected spectrum of a Fibre Bragg grating (FBG) undergoes a splitting of the single peak of the Bragg wavelength. In this work, we employed the Transfer Matrix Method (TMM) for x- and y-polarized wave-modes to model the uniform FBG reflection spectra for uniform and non-uniform transverse loads. We also performed experimental measurements for two different transverse load scenarios. The load profiles chosen for these experiments were applied on the FBG sensor through a block of steel and a roll bearing pin. Then, the modelled and …