5 papers
Quantum kinetic theory: correlations and linking
John Hannay
Classically the kinetic theory for a perfect gas has zero spatial number density correlation between separate points because the particles are independent. But the joint spatial an…
The correlated linking numbers of a Brownian loop with two arbitrary curves
J. H. Hannay
The standard kinetic path integral for all spatially closed Brownian paths (loops) of duration t weighted by the product mn is evaluated, where m and n are the linking numbers of t…
Winding number correlation for a Brownian loop in a plane
J. H. Hannay
A Brownian loop is a random walk circuit of infinitely many, suitably infinitesimal, steps. In a plane such a loop may or may not enclose a marked point, the origin, say. If it doe…
Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane
Olivier Giraud, Andy Thain, John H. Hannay
The shrunk loop theorem presented here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a…
Exact scattering theory for any straight reflectors in two dimensions
J. H. Hannay, A. Thain
The exact Green function for the scalar wave equation in a plane with any set of perfectly reflecting straight mirrors, which may be joined to form corners, is given as a diffracti…