Approximations by Graphs and Emergence of Global Structures |
| P. Exner a,b, P. Hejčík c and P. Šeba b,c
aNuclear Physics Institute, Czech Academy of Sciences, 25068Řežnear Prague, Czechia bDoppler Institute, Czech Technical University, Břehová 7, 11519 Prague, Czechia cUniversity of Hradec Králové, Ví ta Nejedého 573, 50002 Hradec Králové, Czechia |
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| Received: 19 05 2005; |
| We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wave functions approximate solutions of the Schrödinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature. |
| DOI: 10.12693/APhysPolA.109.23 PACS numbers:03.65.Nk |