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The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. [1][2] This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors. The reflection of light from a single interface between ...
Transfer matrix. In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory. For the mask , which is a vector with component indexes from to , the ...
Transfer-matrix method. In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. [ 1][ 2] In many one dimensional lattice models, the partition function is first written as an n -fold ...
Transfer function matrix. In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. [ 1] The matrix relates the outputs of the system to its inputs.
A corner transfer matrix A 2 m (defined for an m×m quadrant) may be expressed in terms of smaller corner transfer matrices A 2 m-1 and A 2 m-2 (defined for reduced (m-1)×(m-1) and (m-2)×(m-2) quadrants respectively). This recursion relation allows, in principle, the iterative calculation of the corner transfer matrix for any lattice quadrant ...
Quantum Heisenberg model. The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. It is related to the prototypical Ising model, where at each site ...
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller . In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix .
Realization (systems) In systems theory, a realization of a state space model is an implementation of a given input-output behavior. That is, given an input-output relationship, a realization is a quadruple of (time-varying) matrices such that. with describing the input and output of the system at time .