Sökning: "quantum graphs"
Visar resultat 1 - 5 av 10 avhandlingar innehållade orden quantum graphs.
1. Extremal eigenvalues and geometry of quantum graphs
Sammanfattning : This thesis consists of four papers concerning topics in the spectral theory of quantum graphs, which are differential operators on metric graphs.In paper I we present a family of graphs with an arbitrary number of cycles for which a certain eigenvalue upper estimate is sharp. LÄS MER
2. Quantum Graphs and Equi-transmitting Scattering Matrices
Sammanfattning : The focus of this study is scattering matrices in the framework of quantum graphs,more precisely the matrices which describe equi-transmission. They are unitary andHermitian and are independent of the energies of the associated system. LÄS MER
3. Spectral estimates and Ambartsumian-type theorems for quantum graphs
Sammanfattning : This thesis consists of four papers and deals with the spectral theory of quantum graphs. A quantum graph is a metric graph equipped with a self-adjoint Schrödinger operator acting on functions defined on the edges of the graph subject to certain vertex conditions. LÄS MER
4. Higher order differential operators on graphs
Sammanfattning : This thesis consists of two papers, enumerated by Roman numerals. The main focus is on the spectral theory of -Laplacians. Here, an -Laplacian, for integer , refers to a metric graph equipped with a differential operator whose differential expression is the -th derivative. LÄS MER
5. On Aspects of Anyons and Quantum Graphs
Sammanfattning : This thesis consists of two distinct parts. The first part, based on the first two accompanied papers, is in the field of topological phases of matter and the second part, based on the third accompanied paper, looks at a problem in the field of quantum graphs, a rapidly growing field of mathematical physics. LÄS MER