Field-theoretic approach to Quantum Graphs: Universal Spectral Statistics and Quantum Ergodicity

28 May 2008, 3 pm

 

Speaker: Professor Sven Gnutzmann (Nottingham)

I will present a field-theoretic approach to quantum graphs based on a supersymmetric sigma-model on graphs. The power of that approach will be discussed for two applications: universal (random-matrix) spectral statistics and quantum ergodiciity. In both cases a saddle-point analysis to a sigma model on a quantum graph yields a "physicists' proof" of universality for large well-connected graphs together with explicit conditions that relate universality to a corresponding classical dynamics. If time allows I will discuss the possiblities to obtain new rigorous results (though more modest than spectral statistics or quantum ergodicity) using this approach.