6 papers
Closed geodesics in homology classes on random hyperbolic surfaces of large genus
Zeev Rudnick
We study the distribution of closed geodesics in homology classes on random hyperbolic surfaces of large genus. Viewing the surface as a random point in moduli space equipped with…
The classification of real quadratic fields which satisfy Hammarhjelm's condition
Zeev Rudnick
A real quadratic field satisfies Hammarhjelm's condition if its ring of integers has unique factorization, and the Minkowski lattice of its ring of integers contains no point in a…
Closed geodesics in short intervals for random hyperbolic surfaces
Zeev Rudnick
We study the distribution of closed geodesics in short intervals on random hyperbolic surfaces of large genus, and compare it with the classical problem of primes in short interval…
On quantum ergodicity for higher dimensional cat maps
Pär Kurlberg, Alina Ostafe, Zeev Rudnick +1
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z…
The density conjecture for Juddian points for the quantum Rabi model
Rishi Kumar, Zeév Rudnick
We study doubly degenerate (Juddian) eigenvalues for the Quantum Rabi Hamiltonian, a simple model of the interaction between a two-level atom and a single quantized mode of light.…
The Quantum Rabi model: Towards Braak's conjecture
Zeév Rudnick
We establish a density one version of Braak's conjecture on the fine structure of the spectrum of the quantum Rabi model, as well as a recent conjecture of Braak, Nguyen, Reyes-Bus…