• Corpus ID: 118979169

Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions

@article{Ershova2014TraceFF,
  title={Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions},
  author={Yulia Yu. Ershova and Alexander V. Kiselev},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $\delta$ type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of $L_1$ and $C^M$ edge potentials) are obtained which link together two different quantum graphs under the assumption… 
View PDF on arXiv
7 Citations
Methods Citations
3

7 Citations

Isospectrality for graph Laplacians under the change of coupling at graph vertices

Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace…

The Krein–von Neumann Extension for Schrödinger Operators on Metric Graphs

The Krein–von Neumann extension is studied for Schrödinger operators on metric graphs. Among other things, its vertex conditions are expressed explicitly, and its relation to other self-adjoint…

ON INVERSE TOPOLOGY PROBLEM FOR LAPLACE OPERATORS ON GRAPHS

Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ type. Under one additional assumption, the inverse…

ISOSPECTRALITY FOR GRAPH LAPLACIANS UNDER THE CHANGE OF COUPLING AT GRAPH VERTICES: NECESSARY AND SUFFICIENT CONDITIONS

Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are ofand � ' types. Assuming rational in- dependence of edge lengths,…

Spectral enclosures for non-self-adjoint extensions of symmetric operators

Boundary Value Problems, Weyl Functions, and Differential Operators

The book under review is a comprehensive treatment of boundary value problems from the unifying point of view of boundary triplets, offering a panoramic view ranging from abstract problems to…

Behrndt, Jussi and Langer, Matthias and Lotoreichik, Vladimir and Rohleder, Jonathan (2018) Spectral enclosures for non-self-adjoint

Article history: Received 20 October 2017 Accepted 11 April 2018 Available online 3 May 2018 Communicated by K. Seip MSC: 47A10 35P05 35J25 81Q12 35J10 34L40 81Q35

References

SHOWING 1-10 OF 34 REFERENCES

Trace formulae for graph Laplacians with applications to recovering matching conditions

Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an…

Inverse problems for quantum trees II:Recovering matching conditions for star graphs

The inverse problem for the Schrodinger operator on a star graph is investigated. It is proven that such Schrodinger operator, i.e. the graph, the real potential on it and the matching conditions at…

Inverse problems for quantum trees

Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices. These inverse problems are connected with…

Inverse problems on graphs: recovering the tree of strings by the BC-method

A planar graph consisting of strings of variable densities is considered. The spectrum of the Dirichlet problem on the graph and the values of derivatives of the normalized eigenfunctions at the…

Heat kernels on metric graphs and a Trace Formula

We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are…

Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

Abstract We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix…

Inverse spectral problem for quantum graphs

The inverse spectral problem for the Laplace operator on a finite metric graph is investigated. It is shown that this problem has a unique solution for graphs with rationally independent edges and…

Inverse problems for Aharonov–Bohm rings

  • P. Kurasov
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2009
Abstract The inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It…

Can one hear the shape of a graph

We show that the spectrum of the Schroperator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the…

On revealing graph cycles via boundary measurements

This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or…