Neutron Fluctuations

CHAPTER TWO

GENERALISATION OF THE PROBLEM

Contents

2.1 Joint Distribution of Particle Numbers at Different Time Instants

2.2 Branching Process with Two Particle Types

2.3 Extinction and Survival Probability

2.1 JOINT DISTRIBUTION OF PARTICLE NUMBERS AT DIFFERENT TIME INSTANTS

Let t₁ = t and t₂ = t + u be two time instants where u ≥ 0. Let n(t₁) and n(t₂) denote the number of particles present in a multiplying system at the time instants t₁ and t₂, respectively. Then,

(2.1)

is the probability that in the multiplying system, n₁ particles are present at t₁ and n₂ particles at t₂ ≥ t₁, provided that one particle existed in the system at t = ...