We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well potential. The convergence proof is based on the Rayleigh principle of the underlying Wasser-stein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.

We consider the problem of quantum ‘‘reflection above the barrier,’’ introducing a distorted-wave Born approximation based on the primitive semiclassical Wentzel-Kramers-Brillouin wave function. The idea generalizes to the concept of an unperturbed Hamiltonian defined as the exact Hamiltonian plus small parts which ‘‘turn off’’ nonclassical processes such as barrier reflection and barrier tunne...

We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding o...

It is shown that price changes of the U.S. dollar-German mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore, we show how Kramers-Moyal coefficients can be estimated from the empirical data. Finally, we present an explicit Fokker-Planck equation which models very precisely the empirical probability distributions, in particular, their non...

The reflectance of single crystal LaSrGaO 4 has been measured from ≈ 50 to 40000 cm −1 along the a andc axis. The optical properties have been calculated from a Kramers-Kronig analysis of the reflectance for both polarization. The reflectance curves have been fit using a product of Lorentzian oscillators.

According to the Smoluchowski-Kramers approximation, the solution of the equation μq̈ t = b(q μ t ) − q̇ t + Σ(q t )Ẇt, q 0 = q, q̇ 0 = p converges to the solution of the equation q̇t = b(qt) + Σ(qt)Ẇt, q0 = q as μ → 0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.

Wave propagation in a one-dimensional random medium with shortor long-range correlations is analyzed. Multiple scattering is studied in the regime where the fluctuations of the medium parameters are small and the propagation distance is large. In this regime pulse propagation is characterized by a random time shift described in terms of a standard or fractional Brownian motion and a determinist...

H.-J. Kull† Institute of Theoretical Physics A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany (Dated: October 14, 2009) Abstract The time-dependent, single-particle Schrödinger equation with a finite-range potential is solved numerically on a three-dimensional spherical domain. In order to correctly account for outgoing waves, perfect reflection-free radiation boundary conditi...