# Transition from a network of thin fibers to the quantum graph : an explicitly solvable model

@inproceedings{Molchanov2006TransitionFA, title={Transition from a network of thin fibers to the quantum graph : an explicitly solvable model}, author={Stanislav Molchanov and Boris Vainberg}, year={2006} }

- Published 2006

We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain Ωε with the Dirichlet boundary conditions on ∂Ωε. The transition from the solutions of the scattering problem on Ωε to the solutions of a problem on the limiting quantum graph Γ is studied. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problem on the limiting graph. If the frequency of the incident wave is above the bottom of… CONTINUE READING

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## Thin tubes in mathematical physics , global analysis and spectral geometry

View 2 Excerpts

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#### References

##### Publications referenced by this paper.

Showing 1-10 of 14 references

## Branched quantum wave guides with Dirichle BC: the decoupling case

View 3 Excerpts

## Post , Convergence of spectra of graphlike thin manifolds

## Zeng , Convergence of spectra of mesoscopic systems collapsing onto a graph

## Asymptotics of spectra of Neumann Laplacians in thin domains, in Advances in Differential Equations and mathematical Physics, Yu

View 3 Excerpts

## Convergence of spectra of mesoscopic systems collapsing onto a graph

View 2 Excerpts

## Variational problems on myltiply connected thin strips. I. Basic estimates and convergence of the Laplacian spectrum, Arch

View 2 Excerpts

## Zeng , Asymptotics of spectra of Neumann Laplacians in thin domains , in Advances in Differential Equations and mathematical Physics , Yu

## Schrödinger operators on graphs and symplectic geometry, The Arnold fest

View 1 Excerpt