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The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application
Linear coupled matrix equations are widely utilized in applications, including stability analysis of control systems and robust control. In this...
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Direct solution of multiple excitations in a matrix product state with block Lanczos
AbstractMatrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one...
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Scattering Problems with No Exact Solution II: The Resolvent Matrix, the H-Matrix, and the I-Matrix
For problems with no exact solution, it is still possible to define a half-space auxiliary matrix X(z), as we have shown in the Chap....
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The Matrix Perturbation Method
The Matrix Perturbation Method is presented as a novel technique for obtaining approximate solutions to the Schrödinger equation in non-relativistic...
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Mueller Matrix Imaging
Polarimetric imaging is a technique of great interest to study fiber-like macromolecules present in biological tissues. As they exhibit a certain...
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4 × 4 Transfer Matrix T p for Dielectric Homogeneous Films
The matrix Δ in (A.5) does not depend on z if the medium is homogeneous, i.e., ɛ is not a function of z. The solution of (A.2) for a layer with...
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Examples of the Matrix Perturbation Method
In this chapter we present several examples of the Matrix Perturbation Method. First, we analyze the harmonic oscillator perturbed by a linear...
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Gibbsite- and kuzelite-based matrix for the preservation of radioactive aqueous sodium nitrate concentrates
The article studies the possibility of using a matrix of gibbsite and kuzelite for the preservation of liquid radioactive wastes consisting of...
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Analytic and numerical bootstrap for one-matrix model and “unsolvable” two-matrix model
We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large N limit, develo** and improving the...
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Cauchy problems related to integrable matrix hierarchies
AbstractWe discuss the solvability of two Cauchy problems in matrix pseudodifferential operators. The first is associated with a set of matrix...
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4×4 Transfer Matrix T p for Isotropic Films
Isotropic materials can be treated much easier and by simpler equations than through the 4×4 approach. However, the isotropic solution within the 4×4...
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Applications of the Matrix Perturbation Method
This chapter provides an explicit expression for the second-order perturbative solution of a single trapped ion at the high intensity regime. Unlike...
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Reconstructing S-matrix Phases with Machine Learning
An important element of the S -matrix bootstrap program is the relationship between the modulus of an S -matrix element and its phase. Unitarity...
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Analysis of the Vibrational Process Inside an Acoustic Interference Array Using the Reverberation Matrix Method
The theoretical study of sound field formation in an acoustic interference array presented in this article is motivated by an analysis of the...
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Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry
We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models...
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Matrix Mechanics
In 1925, with a stroke of genius stemming from his previous work on light dispersion, W. Heisenberg[aut]Heisenberg, Werner Karl managed to dissipate...
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Two-State Systems, Matrix Mechanics
In the previous chapter, we saw how Heisenberg’s matrix mechanics arose in 1924–1925. What we want to do here is consider the problem of the NH...
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On solutions of matrix soliton equations
AbstractWe show that all local holomorphic solutions of matrix soliton equations of parabolic type admit an analytic continuation to globally...
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An Eshelbian Homogenization Solution for the Coupled Mechanical-Diffusion Problem
AbstractWhen alloying elements diffuse into a metallic matrix, the matrix phase usually transforms into an inclusion phase. The phase transformation...
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Solution of Relativistic Feshbach–Villars Spin-1/2 Equations
We propose a computational method for relativistic spin-1/2 particles by solving the corresponding Feshbach–Villars equation. We have found that the...