35 citations · 128 across the 7 of their papers we have counts for
7 papers
Stability of spectral partitions and the Dirichlet-to-Neumann map
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +1
The oscillation of a Laplacian eigenfunction gives a great deal of information about the manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, a…
Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
G. Berkolaiko, J. Kuipers
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport…
Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
G. Berkolaiko, J. Kuipers
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix a…
On inequivalent factorizations of a cycle
G. Berkolaiko, J. M. Harrison, M. Novaes
We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 ... n) into a product of smaller cycles of given length, on one side, and trees of a certai…
Quantum ergodicity for graphs related to interval maps
G. Berkolaiko, J. P. Keating, U. Smilansky
We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v.…
No quantum ergodicity for star graphs
G. Berkolaiko, J. P. Keating, B. Winn
We investigate statistical properties of the eigenfunctions of the Schrodinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctio…
Swelling-collapse transition of self-attracting walks
A. Ordemann, G. Berkolaiko, S. Havlin +1
We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence for a transition analogous to the…