The classical noise activated equilibration process for a particle moving in a metastable potential well is considered as an eigenproblem. The smallest nonzero real eigenvalue of Kramers' Fokker-Planck model is evaluated analytically by means of Rayleigh's quotient. The treatment allows both for...

The exact dynamical solution is given for a harmonically bound particle of finite size (the oscillator) coupled rigidly to a finitely extended two-dimensional mechanical continuum transmission line (the membrane). A quantum mechanical ultraviolet divergence in the particle's momentum...

The real-time dynamics of the asymmetric two-state system weakly interacting with a thermal environment is derived in a rather simple yet novel manner in the Heisenberg picture. Through second order in the coupling coefficients general formulae are obtained (i) for the quantum coherence...

In this paper we embark once more on the current discussion concerning the appropriate expression for the Lagrangian occurring in the action in the functional integral representation of continuous Markov processes. The equivalent differential equation representation of diffusion processes, that...

Using a nonlinear projection operator technique, the Markovian stochastic dynamics of a classical Brownian particle is derived in the case that the effective temperature is not constant. After recapitulating the general formalism and its application to isothermal Brownian motion, an isolated...

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...