Time-independent Matrix Research Articles

Model for Characterization and Optimization of Spectrally Selective Structures to Reduce the Operating Temperature and Improve the Energy Yield of Photovoltaic Modules

Many existing commercially manufactured photovoltaic modules include a cover layer of glass, commonly coated with a single layer antireflection coating (ARC) to reduce reflection losses. As many common photovoltaic cells, including c-Si, CdTe, and CIGS, decrease in efficiency with increasing temperature, a more effective coating would increase reflection of sub-bandgap light while still acting as an antireflection coating for higher energy photons. The sub-bandgap reflection would reduce parasitic sub-bandgap absorption and therefore reduce operating temperature. This reduction under realistic outdoor conditions would lead to an increase in annual energy yield of a photovoltaic module beyond what is achieved by a single layer ARC. However, calculating the actual increase in energy yield provided by this approach is difficult without using time-consuming simulation. Here, we present a time-independent matrix model which can quickly determine the percentage change in annual energy yield of a module with a s...

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

A new dynamic-system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on first-hand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), employs a dynamical system formality using a global sparse matrix, which characterizes the physical, optical and geometrical properties of the material-volume of interest. The new system state is generated by the above time-independent matrix, using simple matrix-vector multiplication for each subsequent time step. DRTS is capable of calculating accurately the time evolution of photon propagation in media of complex structure and shape. The flexibility of DRTS allows the integration of time-dependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. Various examples of DRTS simulation results are presented for ultra-fast light pulse 3-D propagation, demonstrating greatly reduced computational cost and resource requirements compared to other methods.

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as lightfront parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially non-local correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the LSZ reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Finally we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.

Bjorken-x Dependence of Hadronic Structure from Lattice QCD

I present a first direct lattice-QCD calculation of the Bjorken-x dependence of hadron structure functions. By taking a hadron with a large momentum boost, we are able to connect light-cone quantities to lattice-QCD nonlocal but time-independent matrix elements. Since the largest attainable momentum is limited, we correct for the sizable leading momentum dependence systematically. In this talk, I present an exploratory study of the nucleon quark density, helicity and transversity distributions.

On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.

New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation

A propagation method for the time dependent Schrödinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde’s usually results in system of ode’s of the form 0.1 $$u_t - G u =s$$ where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schrödinger equation with time-dependent potential and to non-linear Schrödinger equation will be presented.

Exploring the top and bottom of the quantum control landscape

A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability P(i → f) between the states of a finite level quantum system. Traditionally, the controls are applied fields; here, we extend the notion of control to also include the Hamiltonian structure, in the form of time independent matrix elements. Level sets of controls that produce the same transition probability value are shown to exist at the bottom P(i → f)=0.0 and top P(i → f)=1.0 of the landscape with the field and/or Hamiltonian structure as controls. We present an algorithm to continuously explore these level sets starting from an initial point residing at either extreme value of P(i → f). The technique can also identify control solutions that exhibit the desirable properties of (a) robustness at the top and (b) the ability to rapidly rise towards an optimal control from the bottom. Numerical simulations are presented to illustrate the varied control behavior at the top and bottom of the landscape for several simple model systems.

Parametric resonance in systems with small dissipation

A linear oscillatory system having multiple degrees of freedom with periodic coefficients is considered. The system involves three independent parameters: the frequency and amplitude of the periodic exitation and a parameter of the dissipative forces, the last two being assumed small. Instability of the trivial solution (parametric resonance) is investigated. For an arbitrary periodic exitation matrix and a positive-definite matrix of the dissipative forces, general expressions are obtained for the domains of fundamental and combination resonances. Two special cases of the periodic exitation matrix, frequently encountered in applications, are studied: a symmetric matrix, and a time-independent matrix multiplied by a scalar periodic function. It is proved that in the first case the system is subject only to fundamental and sum-type combination resonances; in the second case fundamental resonance and sum or difference type combination resonance may occur, depending on the sign of a certain constant. It is shown that in both cases the resonance domains in the first approximation are cones in three-dimensional parameter space. Examples considered are the problem of the dynamic stability of a two-dimensional bending mode of an elastic beam subject to periodic torques, and the problem of the stability of an elastic rod of variable cross-section compressed by a periodic longitudinal force.

Micromechanics effects in creep of metal-matrix composites

The creep of metal-matrix composites is analyzed by finite element techniques. An axisymmetric unit-cell model with spherical reinforcing particles is used. Parameters appropriate to TiC particles in a precipitation-hardened (2219) Al matrix are chosen. The effects of matrix plasticity and residual stresses on the creep of the composite are calculated. We confirm (1) that the steady-state rate is independent of the particle elastic moduli and the matrix elastic and plastic properties, (2) that the ratio of composite to matrix steady-state rates depends only on the volume fraction and geometry of the reinforcing phase, and (3) that this ratio can be determined from a calculation of the stress-strain relation for the geometrically identical composite (same phase volume and geometry) with rigid particles in the appropriate power-law hardening matrix. The values of steady-state creep are compared to experimental ones (Krajewskiet al.). Continuum mechanics predictions give a larger reduction of the composite creep relative to the unreinforced material than measured, suggesting that the effective creep rate of the matrix is larger than in unreinforced precipitation-hardened Al due to changes in microstructure, dislocation density, or creep mechanism. Changes in matrix creep properties are also suggested by the comparison of calculated and measured creep strain rates in the primary creep regime, where significantly different time dependencies are found. It is found that creep calculations performed for a timeindependent matrix creep law can be transformed to obtain the creep for a time-dependent creep law.

An Approximate Technique for Dynamic Elastic-Plastic Analysis

The possibility of obtaining an approximate sufficiently reliable response for elasticplastic discretized structures subjected to dynamic load (kinematical and/or mechanical), with alow computational effort, has been considered. A suitable technique to this effect comes from the form of the dynamic influence matrix of imposed plastic strains on self-stresses, which is shaped by adding up a sparse time-dependent matrix and a block diagonal time-independent matrix (which is the sum of two block diagonal matrices). Several cases of practical interest have been studied, among these cases a special one where all the degrees-of-freedom are dynamic. The technique is compared to other approximate techniques. The structures the elements of which have monodimensional elastic domain are considered with special attention.