The noise spectra of y(r, t) governed by (∂/∂t + λ)y(r, t) = ξ(r, t), where ξ is a volume Langevin source, are expressed with the aid of the Fourier-Laplace transformed Green's function G. We give the response form (quadratic in G) and the correlation form (linear in G plus quadratic...

A class of essentially non-equilibrium distributions characterized by the constant flux of one of the “integral of motion” (e.g. energy, number of particles or momentum) both for waves and particles is shown to exist in plasmas due to the symmetry of collision integrals (particle-wave...

In this paper a general group theoretical approach is given for the problem of a charged particle moving in an external electromagnetic field F. From a knowledge of the symmetry transformations of the field (Galilean or Poincaré), it is possible to explicitly construct groups of operators which...

The existence of the asymptotic collision operator ψ(0) is established for a class of observables. Sufficient conditions are given for the vanishing of ψ(0) and for the existence of collisional and non-collisional invariants.

The diffusive escape rate out of a potential well is studied. Kramers' original method is compared with the result of an eigenfunction analysis of the Smoluchowski equation for diffusion in a double well potential. It is shown that by evaluating exactly two integrals, calculated by Kramers in a...

The classical one-dimensional Heisenberg magnet is treated in the context of renormalization theory. This treatment is shown to be equivalent to the usual transfer matrix approach. If the chain consists of N spins, the original hamiltonian will, upon repeated application of the renormalization...

It has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was...

The Mori scheme for dealing with the description for the time evolution of a many body system towards its equilibrium state is used to construct a set of coarse grained or mesoscopic variables whose dynamics is uniquely connected with the corresponding microscopic dynamic operator. Also, the...

R.L. Stratonovich has given a derivation of kinetic equations, if a stochastic process is determined by a system of fluctuation equations. In this paper it is examined how the equations of motion of a particle of a system of mass points can be interpreted as a system of fluctuation equations....

It is shown that the extremal phase-space representations of quantum mechanics can be expressed in terms of wave-functions on L2-spaces which are embedded in L2(Γ). In L2(Γ) all these representations are restrictions of a globally defined representation of the canonical commutation relations....