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Accueil > Rubrique hors menu > Événements > Actualités > Séminaire

Colloque CPTGA

Leszek Sirko (Institute of Physics of the Polish Academy of Sciences)
Properties of open quantum graphs and microwave networks
Lieu : Amphithéâtre, maison des Magistères,
le vendredi 15 novembre 2019 à 11h00
Personne à contacter : Julia Meyer ()

We will discuss interesting properties of open quantum graphs and microwave networks [1]. We will demonstrate that there exist graphs which do not obey the Weyl’s law N(R) = LR/π + O(1), where O(1) is a function which for R going to infinity is bounded by a constant. The Weyl’s law directly links the counting function N(R) of the number of resonances with the square root of energy k, 0(k), and the total length L of the internal edges of a graph. Graphs which do not obey the Weyl’s law are called non-Weyl graphs. We show that for standard coupling conditions the transition from a Weyl graph to a non-Weyl graph occurs if we introduce a balanced vertex. A vertex of a graph is called balanced if the numbers of infinite leads and internal edges meeting at a vertex are the same. The experimental results demonstrating the existence of non-Weyl networks are in excellent agreement with the theoretical predictions [2].

Acknowledgements

This work was supported in part by the National Science Centre, Poland, Grant No. 2016/23/B/ST2/03979 and the Operational Programme Innovative Economy Grant No. POIG.01.01.02-00-008/08. J. L. was supported by the internal grant project “Introduction to quantum mechanics on graphs” of the University of Hradec Kralove.

References

  • [1]. O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, and L. Sirko, Phys. Rev. E 69, 056205 (2004).
  • [2]. M. Ławniczak, J. Lipovsky, and L. Sirko, Phys. Rev. Lett. 122, 140503 (2019).


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