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...

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 dynamical problem of a harmonically bound nonrelativistic electron with standard dipole model coupling to the electromagnetic field in a finite region of three-dimensional space is solved exactly in a simple and (in the realm) novel manner. The emphasis is on a Lagrangian real space...

It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1)...

The sum over paths for a generalized Wiener diffusion process has been presented in a previous paper on the basis of the concept of time-local gaussian processes. This well-defined functional sum leads to a functional integral for the probability of passing from an initial state to some final...