Fermionic stochastic differential equations and the index of Fredholm operators

The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise.     

On a Class of Non-Translation Invariant Feller Semigroups on Lie Groups

We consider a class of Feller semigroups on Lie groups which fail to commute with left translation due to the existence of a cocycle h which is identically one for Lévy processes. Under certain conditions, we are able to show that the infinitesimal generator of such a semigroup has the Lévy–Khintchine–Hunt form but with variable characteristics, thus we obtain an extension of classical work in Euclidean space by Courrège.     

On a class of stochastic flows driven by quantum Brownian motion

A class of quantum stochastic flows on^*-algebras is introduced which includes both classical flows on Riemannian manifolds and flows induced by Lie group actions onC ^*-algebras. Criteria are established to determine those flows which are unitarily equivalent to ones driven by classical Brownian motion. It is shown that taking complex combinations of the driving coefficients of such flows gives rise to flows which are not of Evans-Hudson type (i.e., all driving coefficients do not preserve the relevant algebra).     

Unitary evolutions and horizontal lifts in quantum stochastic calculus

Unitarity is proved for a class of solutions of quantum stochastic differential equations with unbounded coefficients. The resulting processes are then used to construct algebraic quantum diffusions. Applications include an existence proof for a class of diffusions on the non-commutative two-torus and a geometric interpretation for diffusions driven by the classical Poisson process.     

THE CHEMILUMINESCENT NO—O-ATOM REACTION

Abstract— New additional experimental data were obtained to give further information pertinent to the mechanism for the chemiluminescent NO—O-atom reaction. Results were obtained for the change of emission intensities from 10 to 300 microns pressure. Some studies were also made of the effect of various third bodies. The results support a simple two body recombination for the mechanism for the light emission: NO+O + NO₂+ hv .     

Levy flows on manifolds and operator algebras

Translated from Matematicheskie Zametki, Vol. 54, No. 4, pp. 3–11, October, 1993.     

Some <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> properties of semigroups of measures on Lie groups

We investigate the induced action of convolution semigroups of probability measures on Lie groups on the L ²-space of Haar measure. Necessary and sufficient conditions are given for the infinitesimal generator to be self-adjoint and the associated symmetric Dirichlet form is constructed. We show that the generated Markov semigroup is trace-class if and only if the measures have a square-integrable density. Two examples are studied in some depth where the spectrum can be explicitly computed, these being the n-torus and Riemannian symmetric pairs of compact type.