18 citations · 105 across the 29 of their papers we have counts for
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Scarring for Quantum Maps with Simple Spectrum
Dubi Kelmer
We previously introduced a family of symplectic maps of the torus whose quantization exhibits scarring on invariant co-isotropic submanifolds. The purpose of this note is to show t…
Quantum Ergodicity for products of hyperbolic planes
Dubi Kelmer
For manifolds with geodesic flow that is ergodic on the unit tangent bundle, the quantum ergodicity theorem implies that almost all Laplacian eigenfunctions become equidistributed…
Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms
Dubi Kelmer
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. Th…
Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus
Dubi Kelmer
We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribution in the semiclassical limit. We construct super-scars tha…
On the quantum variance of matrix elements for the cat map on the 4-dimensional torus
Dubi Kelmer
For many classically chaotic systems, it is believed that in the semiclassical limit, the matrix elements of smooth observables approach the phase space average of the observable.…