54 citations · 115 across the 4 of their papers we have counts for
4 papers
Quantum ergodicity for quantum graphs without back-scattering
Matthew Brammall, Brian Winn
We give an estimate of the quantum variance for -regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expand…
Quantum graphs where back-scattering is prohibited
J. M. Harrison, U. Smilansky, B. Winn
We describe a new class of scattering matrices for quantum graphs in which back-scattering is prohibited. We discuss some properties of quantum graphs with these scattering matrice…
On occurrence of spectral edges for periodic operators inside the Brillouin zone
J. M. Harrison, P. Kuchment, A. Sobolev +1
The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide oper…
Quantum Variance and Ergodicity for the baker's map
Mirko Degli Esposti, Stéphane Nonnenmacher, Brian Winn
We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker's map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay o…