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The model is named after the Dutch physicist Hendrik Antoon Lorentz. It is a classical, phenomenological model for materials with characteristic resonance frequencies (or other characteristic energy scales) for optical absorption, e.g. ionic and molecular vibrations, interband transitions (semiconductors), phonons, and collective excitations ...
In the case of NMR spectra, the process is relatively straight forward, because the line shapes are Lorentzian, and the convolution of a Lorentzian with another Lorentzian is also Lorentzian. The Fourier transform of a Lorentzian is an exponential. In the co-domain (time) of the spectroscopic domain (frequency) convolution becomes multiplication.
The expression for the imaginary part of complex electrical permittivity, according to the Lorentz model, is a Cauchy distribution. As an additional distribution to model fat tails in computational finance, Cauchy distributions can be used to model VAR (value at risk) producing a much larger probability of extreme risk than Gaussian ...
By comparison, based on the concept of attractor coexistence within the generalized Lorenz model [26] and the original Lorenz model ([36] [37]), Shen and his co-authors [35] [38] proposed a revised view that “weather possesses both chaos and order with distinct predictability”. The revised view, which is a build-up of the conventional view ...
Lorentzian may refer to Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution; Lorentz lineshape ...
The Lorentzian profile has no moments (other than the zeroth), and so the moment-generating function for the Cauchy distribution is not defined. It follows that the Voigt profile will not have a moment-generating function either, but the characteristic function for the Cauchy distribution is well defined, as is the characteristic function for ...
Just as Euclidean space can be thought of as the local model of a Riemannian manifold, Minkowski space, with the flat Minkowski metric is the local model of a Lorentzian manifold. Likewise, the model space for a pseudo-Riemannian manifold of signature (p, q) is pseudo-Euclidean space,, for which there exist coordinates x i such that
The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap .