8 papers
Poisson statistics via the Chinese remainder theorem
A. Granville, P. Kurlberg
We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem.…
Lattice Points on Circles and Discrete Velocity Models for the Boltzmann Equation
L. Fainsilber, P. Kurlberg, B. Wennberg
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice po…
On the distribution of matrix elements for the quantum cat map
P. Kurlberg, Z. Rudnick
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phas…
On a character sum problem of H. Cohn
Par Kurlberg
Let be a complex valued function on a finite field such that , , and for . Cohn asked if it follows that is a nontrivial mult…
Value distribution for eigenfunctions of desymmetrized quantum maps
Par Kurlberg, Zeev Rudnick
We study the value distribution and extreme values of eigenfunctions for the ``quantized cat map''. This is the quantization of a hyperbolic linear map of the torus. In a previous…
On quantum ergodicity for linear maps of the torus
P. Kurlberg, Z. Rudnick
We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (``cat maps''). We show that there is a density one sequence of integers so that as N tends…