Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit

Upper bounds on the rate of quantum ergodicity

We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper bound of order |ln ~|−1 on the rate of quantum ergodicity if the classical system is ergodic with a certain rate. In addition we obtain a simila...

Construction of the Classical Limit and Spectral Statistics of Generic Hamiltonian Operators

Spiky Strings and Spin Chains

We determine spectral curves for the known spiky string solutions in AdS space in the limit of large angular momentum. We also construct generic multi-spike solutions in this limit and compute the corresponding spectral data. The resulting spectral curves precisely match those of the classical spin chain describing the dual operators in one-loop gauge theory. Our results confirm the map between...

Quantum chaos with spin-chains in pulsed magnetic fields

Recently it was found that the dynamics in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field can have a close correspondence with the quantum kicked rotor (QKR). The QKR is a key paradigm of quantum chaos; it has as its classical limit the well-known Standard Map. It was found that a single spin excitation could be converted into a pa...

Generic spectral properties of right triangle billiards

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its advantage is its simplicity and explicitness, which allow new insight into the statistical properties of the spectrum. It is shown how the genus of the invariant surface of the classical billiard flow, det...