Exact eigenfunction amplitude distributions of integrable quantum billiards

Duality between quantum and classical dynamics for integrable billiards.

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be o...

On algebraically integrable outer billiards

We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse. In this note, an outer billiard table is a compact convex domain in the plane bounded by an oval (closed smooth strictly convex curve) C. Pick a point x outside of C. There are two tangent lines from x to C; choose one of them, say, the right one...

Exact Amplitude Distributions of Sums of Stochastic Sinusoidals

I consider a model applicable in many communication systems where the sum of n stochastic sinusoidal signals of the same frequency, but with random amplitudes as well as phase angles is present. The exact probability distribution of the resulting signal’s amplitude is of particular interest in many important applications, however the general problem has remained open. I derive new general formu...

Quantum Billiards

Exact S Matrices for Integrable Quantum Spin Chains Luca

We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 spin 1 chain. In addition to having excitations with spin 1/2, this model also has...