N.G. Van Kampen

On the macroscopic theory of Van der Waals forces

A simple macroscopic derivation is given of the non-retarded Van der Waals interaction between two semi-infinite dielectric media.

Eigenvalues of a diffusion process with a critical point

The eigenvalues of a Fokker-Planck equation involving a critical point have been computed by means of a simple discretization technique. The results smoothly connect the monostable case above the critical point with the bistable case below it.

The two expansions of the master equation

Abstract The expansion of the master equation in terms of the jump size leads to either one or two of two different types of Fokker-Planck equations, depending on the kind of system.

The equilibrium distribution of a chemical mixture

Abstract The exact equilibrium distribution of a homogeneous isothermal chemical mixture in a closed vessel is determined. It is not a Poisson distribution, though closely related to it. In addition it is shown to be an exact time-independent solution of the master equation.

Can the Aharonov-Bohm effect transmit signals faster than light?

Abstract It is shown that the well-known magnetic Aharonov-Bohm effect permits the instantaneous transmission of signals. However, its electric counterpart cancels the effect.

Fluctuations in Boltzmann's equation

An equation of Fokker-Planck type is derived for the fluctuations in the momentum space distribution function t(p) of a homogeneous dilute gas.

An equation for the characteristic function of a Markov process and its application to a Langevin process

Abstract For Markov processes a “curtailed characteristic function” is defined. It obeys an equation similar to the master equation. Its solution provides the characteristic function of the process. By applying it to the radioactive decay process the stochastic properties of the corresponding Langevin force are determined.

The expansion of the Fokker-Planck equation including a critical point

The known expansion of the master equation for weak diffusion in an external potential applies to both the monostable and the bistable case, but fails at the critical point. This can be remedied by taking as zeroth order approximation a suitably defined set of eigenfunctions. The resulting expansion is uniformly valid in a range of the pump parameter including the critical point.

Nonlinear transfer equations

The transfer between two thermodynamic systems consists of two unilateral flows, each originating in one of the systems and depending on the thermodynamic state of that system alone. Reciprocity is expressed by the fact that these unilateral flows are derivatives of some functions K of the conjugated forces.