Archiv der Mathematik

, Volume 112, Issue 6, pp 649–659 | Cite as

A remark on the effect of random singular two-particle interactions

  • Joachim KernerEmail author


In this note we study a two-particle bound system (molecule) moving on the positive half-line \({\mathbb {R}}_+\) under the influence of randomly distributed singular two-particle interactions generated by a Poisson process. We give a rigorous definition of the underlying Hamiltonian and study its spectral properties. As a main result we prove that, with finite probability, the random interactions destroy the discrete part of the spectrum which is present in the free system. Most interestingly, this phenomenon is somewhat contrary to the role attributed to random interactions in the context of Anderson localisation where disorder is generally associated with a suppression of transport.


Two-particle system Half-line Quantum graph Singular interaction 

Mathematics Subject Classification

81V70 81Q80 81Q35 81Q10 81Q50 81Q37 


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Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceFernUniversität in HagenHagenGermany

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