Explicit, analytical solution of scaling quantum graphs

Abstract

Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos and quantum chaotic systems are not usually explicitly analytically solvable.

6 pages

References in corpus (5)

• Explicitly solvable cases of one-dimensional quantum chaos
• Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
• One-dimensional quantum chaos: Explicitly solvable cases
• Spectra of regular quantum graphs
• Mathematical Foundations of Regular Quantum Graphs

Cited by in corpus (5)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Green's function approach for quantum graphs: an overview
• The influence of geometry and topology of quantum graphs on their nonlinear-optical properties
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• Scaling and universality in nonlinear optical quantum graphs containing star motifs