The Hamilton equations for a Brownian particle involve its mass as a large parameter. As a consequence its motion is relatively slow and the fast motion of the surrounding fluid molecules can be eliminated by the standard method of eliminating fast variables. The result is equivalent to the...

A systematic expansion method is developed to account for the effect of fluctuations on the motion of a damped Duffing oscillator. The expansion parameter α is the magnitude of the fluctuations. To first order in α we calculate all the correlation functions and the corresponding spectral...

The well-known model of a heavy oscillator interacting with a bath of light oscillators is extended to several heavy oscillators. New features appear when they are in resonance. These are worked out for the case of two identical oscillators, with the following conclusions. If initially one of...

The aim of quantum mechanics is to explain macroscopic, objectively recorded phenomena. Microscopic objects are measured by enabling them to interact with a macroscopic measuring apparatus prepared in a metastable state. Macroscopic objects, such as cats, are not above the laws of quantum...

A model for a Rayleigh particle suspended in a rarefied gas in internal equilibrium is constructed. It is shown that the macroscopic evolution of this system can be described by using nonlinear unilateral transfer flows which are gradients of particular scalar functions. These functions are...

The general formulae derived in an earlier article are applied to some special cases, viz., the Fokker-Planck or diffusion limit, the linear case, and the Malthus-Verhulst equation with random coefficients.

In a recent paper1) a differential equation was studied which involves a stochastic process having the property that all its cumulants are delta-correlated. It is here shown that such processes consist of a random sequence of delta functions with random coefficients. As a consequence the...

The problem of a particle moving in a two-valued random potential occurred in a recent paper by Pomeau. The exact time-dependent solution is here obtained for a quadratic potential by two different methods. The first method treats the problem as a stochastic differential equation and leads to...

A macroscopic system is a quantum system with numerous degrees of freedom. As a consequence the description in terms of individual levels and eigenstates is inappropriate. Rather, the relevant concepts are macrostates and macrovariables. It is shown how to construct these. It is found that on...

The electric current through a membrane has been modelled as a transport process of single charged particles through a pore. In this way the average current and the spectral density of the current fluctuations were computed by Barkai et al. in terms of the behavior of the separate particles. I...