Using Rayleigh's identity for the pertinent eigenvalue of Kramers' Fokker-Planck model, the noise activated rate of escape over a sharp edged potential barrier is obtained for the symmetric double oscillator. The rate is shown in its dependence on barrier height and on viscosity. Both the weak...

A simple sum over paths will be considered for the general nonlinear diffusion process described by complex coordinates. In order to derive the corresponding stochastic differential equation the Feynman method used in quantum mechanics will be generalised for the present case of a coordinate...

Three different types of quantum mechanical barrier systems are considered as eigenvalue problems. First, the real energy levels of the local ground states in a weakly biased double-well potential are determined by connecting wave functions across the barrier. For each energy level the amplitude...

We present a unified treatment for both weak and strong friction — including the turnover regime — of Kramers' Fokker-Planck model for activated rate processes. No recourse to a specific microscopic model (à la Grabert et al.) or Langevin dynamics (à la Graham) will be made. Upon...

The leading anomalous Kolmogorov scaling exponent μθ in the inertial range of temperature spectra is calculated on the basis of a recent theory involving a 4D spectral analysis of fully developed Navier–Stokes–Boussinesq turbulence.

The attention will be focussed on a generalized Wiener diffusion process for which the macroscopic evolution ẙ = c1(y) equals zero, of course, and where the variance of the process obeys g̊s2 = c2(y). The diffusion function c2(y) may be state dependent in an arbitrary way. We invoke our...

The novel (pseudo-)spin hopping analysis of real-time quantum mechanical motion at nonzero temperature in a dissipative double-well potential - as presented in parts I - III - is generalized to include a bias energy between the two wells. The general theory of part I - ab initio based on the...

Using a self-consistent 4D spectral analysis of fully developed Navier–Stokes–Boussinesq turbulence (involving the dynamical response on small scale isotropic configurations) leads to a manyfold ℘(k) for the second-order scaling exponent. Plots of both energy and Reynolds stress spectra...

The quantal form of the classical Liouville equation will be investigated on the basis of a recently developed generalized Hamiltonian theory. The essential novelty inthat theory comprises the use of complex classical coordinates and momenta. We first show how for the nondissipative harmonic...

In this paper we discuss the concept of time-local gaussian processes. These are processes for which the state variable at time t + τ is gaussian distributed around its most probable value at that time, for a specified realization a small time interval τ earlier. On one hand it will be shown...