Stochastic Processes in Quantum Theory and Statistical Physics : Proceedings of the International Workshop Held in Marseille, France, June 29 - July 4,1981

We want to describe the evolution of quantum observables in terms of stochastic jump processes, following a procedure similar to that set up by Maslov [I] and extended by Pb~ Combe et al [2] . To characterize these observables, we shall use the representation by where Je ) ) 0. 4 Conclusion Thus, we have shown that the probabilistic interpretation of Feynman integral ( [I] , [2] ) can be applied to describe the evolution of some classes of observables in a quantum phase space. Formula [5) can be regarded as equivalent to a Feynman integral for this problem. We could have imagined that the stochastic character was specific to the quantum nature of the objects under consideration. However, as it results from the last paragraph, a similar description is also valid for a classical system with a sufficiently regular potential. Quantum theory and non-kolmogorovian probability....Pages 1-12 Stochastic jump processes in the phase space representation of quantum mechanics....Pages 13-18 Transformation of wiener integrals and the desingularization of Coulomb problem....Pages 19-28 Dynamical systems with few degrees of freedom....Pages 29-39 Laplace expansions of conditional wiener integrals and applications to quantum physics....Pages 40-55 Stochastic processes and fermi fields....Pages 56-66 Periodic orbits of dynamical systems with chaotic behavior....Pages 67-74 The Van Hove limit in classical and quantum mechanics....Pages 75-110 Large deviation asymptotics and the polaron....Pages 111-118 All that Brownian motion....Pages 119-135 The diffusion equation and classical mechanics: An elementary formula....Pages 136-146 Stochasticity in non-equilibrium statistical mechanics....Pages 147-153 A stochastic picture of spin....Pages 154-168 On the statistical mechanics of surfaces....Pages 169-199 A note on irreducibility and ergodicity of symmetric markov processes....Pages 200-207 Momentum-position complementarity in stochastic mechanics....Pages 208-215 Non-commutative martingales and stochastic integrals in fock space....Pages 216-222 Some results on the spectra of random schrödinger operators and their application to random point interaction models in one and three dimensions....Pages 223-244 Wiener measures for quantum mechanical path integrals....Pages 245-247 Existence of a first-order phase transition for the Potts model....Pages 248-253 Lagrangians with anticommuting arguments for dirac fields....Pages 254-273 High-temperature path method for a two-dimensional random ising model....Pages 274-280 Stochastic processes in music and art....Pages 281-288 Hopping transport in disordered one-dimensional lattice systems: Random walk in a random medium....Pages 289-303 Large scale behavior of equilibrium time correlation functions for some stochastic ising models....Pages 304-331 Quantum dissipation and stochastic processes....Pages 332-336