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European journal of applied sciences

Bose Statistics of Random Walks on Graphs

Manfred Harringer

Published Jun 25, 2025• 0 citations
Publisher

Abstract

Abstract We build probabilistic process models of motions on a finite graph. For particle statistics, at first we select a particle. Then we build a path of the particle along consecutive edges. Particles are distinguished. Single particles perform Markov chains. For Bose statistics, at first we select an edge as request for a path of a particle along the edge. Particles are not distinguished. The edges are randomly selected by probability weights, or they are triggered by circuits of courses in small steps on circles. We present examples for these process models. We obtain some results, which follow from the balance equation, a refinement of the corresponding balance equation for Markov chains. Quantum mechanics inhibits these process models, because there the annihilation of the zero state is zero.

DOI
10.14738/aivp.1303.18974

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