Approximations by Graphs and Emergence of Global Structures

• Authors: P. Exner , P. Hejčík , P. Šeba
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

03.65.Nk

Discipline

• 03.65.Nk: Scattering theory

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2006
• Volume: 109
• Issue: 1
• Pages: 23-31

Dates

published

2006-01

received

2005-05-19

Contributors

author

P. Exner

• Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řežnear Prague, Czechia
• Doppler Institute, Czech Technical University, Břehová 7, 11519 Prague, Czechia

author

P. Hejčík

• University of Hradec Králové, Víta Nejedého 573, 50002 Hradec Králové, Czechia

author

P. Šeba

• Doppler Institute, Czech Technical University, Břehová 7, 11519 Prague, Czechia
• University of Hradec Králové, Víta Nejedého 573, 50002 Hradec Králové, Czechia

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Identifiers

DOI

10.12693/APhysPolA.109.23