The Onsager-Machlup Lagrangian for diffusion processes in curved spaces is determined by evaluating the covariant path integral by means of a spectral analysis of smooth trajectories in Riemannian normal coordinates. The Lagrangian involves a novel curvature scalar potential term v=−(18)R. The...

In the first article (I) of this series the real-time dynamics of a quantum mechanical (quasi-)particle in a double-well potential coupled to an ohmic environment at nonzero temperature has been studied ab initio on the basis of the Zwanzig-Caldeira-Leggett model Hamiltonian by means of a novel...

The quantum mechanics of a harmonically bound electron with standard dipole model coupling to the electromagnetic field is studied exactly in the limit of zero damping (charge e→0) and infinite field extension (R→∞). In the limit sequence (i) R→∞, (ii) e→0, one obtains Gaussian wave...

Dissipative (ohmic friction coefficient 2λ) and thermal effects in the quantum tunnelling decay rate Γ(λ, T, ε) of a weakly biased (energy |ε|⪡Ub) metastable oscillator (frequency ω0, leaking into free space through a quartic potential energy barrier (height Ub), are found to depend on...

Turbulence mixing by finite size eddies will be treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic closure hypothesis, which implies a well defined recipe for the calculation of sampling and transition rates. The connection with the general...

The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37 (1959) 334]) suffered from a paradox: this resistance erroneously tends to a finite value in the limit of identical solids. We resolve this paradox by calculating...

The decay rate for an unbiased local quasi-equilibrium oscillator, leaking through a quartic potential energy barrier into free space and weakly coupled to an ohmic thermal environment, is calculated in the low temperature quantum tunnelling regime. The imaginary part of the free energy is...

Using a generalized version of Langer's “imaginary part of the free energy” method involving an “extended” bounce and doing a fully “dynamical” evaluation of the weak bias anomalous fluctuation mode, the thermal dependence of the decay rate Γ = A exp(-B) is studied for a metastable...

The quantum decay rate Γ = A exp(−B) of a metastable oscillator is studied for a quartic potential energy barrier model by means of a generalized version of Langer's “imaginary part of the free energy” method in the weak ohmic quantum damping regime. It is found (i) that the fully...

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...