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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear Schrodinger equations on metric graphs
度量图 非线性 薛定谔方程
2023/5/12
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
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
2011/7/26
Motif based hierarchical random graphs: structural properties and critical points of an Ising model.
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....
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 ...
Finding structural anomalies in graphs by means of quantum walks
structural anomalies in graphs quantum walks
2010/10/18
We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes c...
Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
Pauli graphs Hilbert space dimension Dedekind psi function
2010/10/27
We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.
Quaternionic Roots of E 8 Related Coxeter Graphs and Quasicrystals
Quaternionic Roots Quasicrystals E 8 Related Coxeter Graphs
2010/4/19
The lattice matching of two sets of quaternionic roots of F4 leads to quaternionic roots of E8 which has a decomposition H4 + s H4 where the Coxeter graph H4 is represented by the 120 quaternionic ele...