Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472–1475]. For time-reversal invariant systems we obtain the leading terms of the two-point correlation function of the Gaussian symplectic ensemble. Speci...

Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

Symplectic Homology and Periodic Orbits Nearsymplectic Submanifoldskai

Symplectic Homology and Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

A microwave realization of the Gaussian symplectic ensemble