In coloured media, the index of refraction does not decrease monotonically with increasing wavelength, but behaves in a quite non-monotonical way. This behaviour is called anomalous dispersion and results from the fact that the absorption of a material influences its index of refraction. So far, this interesting fact has not been widely acknowledged by the graphics community. In this paper, we ...

The adiabatic evolution of two doubly-degenerate (Kramers) levels is considered. The general five-parameter Hamiltonian describing the system is obtained and shown to be equivalent to one used in the Γ8 ⊗ (τ2 ⊕ ǫ) JahnTeller system. It is shown explicitly that the resulting SU(2) non-Abelian geometric vector potential is that of the (SO(5) symmetric) SU(2) instanton. Various forms of the potent...

Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather...

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H., we show how these equations are related to Langevin equations via the procedure of subor-dination. Introduction. – Some 70 years ago, Kramers [1] considered the motion of a Brownian particle subject to a space-dependent force F(x) per unit mass. His ...

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically inspired examples, these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simul...

We analyze the behavior of a Brownian particle moving in a double-well potential. The escape probability of this particle over the potential barrier from a metastable state toward another state is known as the Kramers problem. In this work we generalize Kramers' rate theory to the case of an environment always out of thermodynamic equilibrium reckoning with non-Markovian effects. We consider a ...

In the Langevin or Ornstein-Uhlenbeck approach to diffusion, stochastic increments are applied to the velocity rather than to the space variable. The density of this process satisfies a linear partial differential equation of the general form of a transport equation which is hyperbolic with respect to the space variable but parabolic with respect to the velocity variable, the Klein-Kramers or s...