Subatomic, High Energy and Plasma Physics seminar: Imre Pazsit

Abstract: The neutron transport equation is associated with a non-self-adjoint (non-Hermitian) operator. Such is the case with operators describing irreversible processes. One can construct an adjoint operator, acting on the adjoint flux ("neutron importance"). Some consequences of the non-Hermitian property and the physical meaning of the adjoint will be discussed. On a wider note, neutron transport is a stochastic process (a branching process), of which the traditional transport equation is the first moment (expectation). A random process can be described by two different master equations (Chapman-Kolmogorov equations) for the evolution of the probability density, namely, by a forward and a backward master equation. At the level of the first moment, these two equations show considerable resemblance to each other, but they become increasingly different with increasing moment order. The purpose of this presentation is to demonstrate this increasing asymmetry and to discuss and interpret the underlying reasons in terms of the increasing order of violating time reversal. Some entertaining pieces of the history of branching processes will also be told.