Quantum graphs: Applications to quantum chaos and universal spectral statistics
S Gnutzmann∥, U Smilansky - Advances in Physics, 2006 - Taylor & Francis
During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …
Graph models for waves in thin structures
P Kuchment - Waves in random media, 2002 - iopscience.iop.org
A brief survey on graph models for wave propagation in thin structures is presented. Such
models arise in many areas of mathematics, physics, chemistry and engineering (dynamical …
models arise in many areas of mathematics, physics, chemistry and engineering (dynamical …
Kirchhoff's rule for quantum wires
V Kostrykin, R Schrader - Journal of Physics A: Mathematical and …, 1999 - iopscience.iop.org
We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph
with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator …
with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator …
Quantum graphs: I. Some basic structures
P Kuchment - Waves in Random media, 2003 - iopscience.iop.org
A quantum graph is a graph equipped with a self-adjoint differential or pseudodifferential
Hamiltonian. Such graphs have been studied recently in relation to some problems of …
Hamiltonian. Such graphs have been studied recently in relation to some problems of …
Periodic orbit theory and spectral statistics for quantum graphs
T Kottos, U Smilansky - Annals of Physics, 1999 - Elsevier
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 …
show that the spectral statistics of fully connected graphs is well reproduced by random …
[图书][B] Analysis on Graphs and Its Applications: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8-June 29, 2007
P Exner - 2008 - books.google.com
This book addresses a new interdisciplinary area emerging on the border between various
areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus …
areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus …
[PDF][PDF] On the spectra of carbon nano-structures
P Kuchment, O Post - arXiv preprint math-ph/0612021, 2006 - arxiv.org
arXiv:math-ph/0612021v4 19 Jan 2007 Page 1 arXiv:math-ph/0612021v4 19 Jan 2007 ON
THE SPECTRA OF CARBON NANO-STRUCTURES PETER KUCHMENT AND OLAF POST …
THE SPECTRA OF CARBON NANO-STRUCTURES PETER KUCHMENT AND OLAF POST …
Quantum graphs: an introduction and a brief survey
P Kuchment - arXiv preprint arXiv:0802.3442, 2008 - arxiv.org
The purpose of this text is to set up a few basic notions concerning quantum graphs, to
indicate some areas addressed in the quantum graph research, and to provide some …
indicate some areas addressed in the quantum graph research, and to provide some …
Realizing discontinuous wave functions with renormalized short-range potentials
T Cheon, T Shigehara - Physics Letters A, 1998 - Elsevier
We show that the most general three-parameter family of point interactions on the line can
be expressed as the self-adjoint local operators in terms of three Dirac's delta functions with …
be expressed as the self-adjoint local operators in terms of three Dirac's delta functions with …