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Asynchronous Quantum Random Walks

Manfred Harringer

Published Sep 25, 2023• 0 citations
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Abstract

Abstract I build random walks on finite graphs Γ(V,E) with vertices V and directed edges E by sequences of randomly selected edges. Edge selection may also be organized by a curve on a torus, observing circuits in both directions of the course at a single circle. The edges trigger state changes of the vertices for particles, bosons or fermions due to the state spaces at the vertices. As a statistical result, I obtain a quantum canonical ensemble together with a vacuum. There are two kinds of process steps, acceptions and rejections, corresponding to stimulated and spontaneous emissions. Such processes are asynchronous versions of time evolution in quantum mechanics.

DOI
10.21203/rs.3.rs-3372215/v3

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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.