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Stationary Nonlinear Schrodinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Nonlinear Schrodinger Equation Simplest Graphs Mathematical Physics
2011/9/29
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Non-equilibrium Steady States of Quantum Systems on Star Graphs
Non-equilibrium Steady States Quantum Systems Star Graphs
2011/7/27
Abstract: Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each e...
Uniform existence of the integrated density of states on metric Cayley graphs
random Schrodinger operator metric graph quantum graph integrated density of states
2011/7/27
Abstract: Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normali...
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs
Systems of Kowalevski type discriminantly separable polynomials quad-graphs
2011/7/27
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs.
Motif based hierarchical random graphs: structural properties and critical points of an Ising model
amenability, degree distribution, clustering, small-world graph, Ising model, critical point
2011/9/15
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D....
Motif based hierarchical random graphs: structural properties and critical points of an Ising model
amenability degree distribution clustering small-world graph Ising model critical point
2011/7/26
Motif based hierarchical random graphs: structural properties and critical points of an Ising model.
Numerical evidence against a conjecture on the cover time of planar graphs
Numerical evidence the cover times of planar graphs Statistical Mechanics
2011/7/28
Abstract: We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time $\tau(G_{N})$ of a planar graph $G_{N}$ o...
Finite propagation speed for solutions of the wave equation on metric graphs
Metric graphs Laplace operators wave equation finite propagation speed
2011/7/25
Abstract: We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The ...