The place of random processes and random fields in quantum theory

C. Syros, C. Schulz-Mirbach

The conventional tacit assumption according to which quantum processes take place in the Newtonian time topology is abandoned. The chronotopological space is based on the interaction proper time neighborhood. It is disconnected, satisfies the separation axioms of the topological space [Formula: see text], and is developed and used to solve some problems related to quantum field theory. In chronotopology the time evolution operator, [Formula: see text], breaks down into the alternative [Formula: see text] = either [Formula: see text]. The unitary, U, and the reduction, R, dynamics are implemented by means of two time evolution operators, [Formula: see text] and [Formula: see text], derived from a quantized version of Gel'fand's theory of the generalized random and infinitely divisible fields. As an application the solution of the paradox of Schrödinger's cat is presented.

Sergio A Albeverio, Ph. Combe, M. Sirugue-Collin

Deng Ling-Ling

In the frame of Ising model, we investigate the critical properties of ferromagnetic spin system with random crystal field and obtain the magnetization expressions for the square lattice by using effective field theory. Special emphasis is placed on critical properties of the system. At the range of concern crystal field and random concentration, the present system shows some new critical properties. We discuss in detail the influence of random concentration on the critical properties and give phase diagram and magnetization curve.

John R. Klauder

Karl-Erik Eriksson

For a microscopic quantum-mechanical system we consider the measurement of an observable A which is assumed to characterize the system uniquely. The measurement process takes place through interaction between the microscopic system and the measurement apparatus, which in turn is influenced by external fields. The detailed influence from the initial state of the measuring apparatus and from the external fields on the density matrix of the microscopic system is stochastic and may be taken into account as a random walk in the simplex characterizing its diagonal elements (in the representation where A is diagonal). The diffusion equation corresponding to this random walk is derived. It is shown that the corners are attractors of this process, i.e. each single measurement ends up in an eigenstate of A . The relative frequencies for the different results are given by the squared moduli of the corresponding amplitudes. The reduction of the wave packet is thus the result of a statistical process.

Takeyuki Hida