On spectral stability of solitary waves of nonlinear Dirac equation on a line (2009)
Berkolaiko, Gregory, Comech, Andrew
We consider the nonlinear Dirac equation in one dimension (the massive Gross-Neveu model). We explicitly construct solitary wave solutions, and then study the linearization of the equation at a...
Moments of the Wigner delay times (2009)
Berkolaiko, Gregory, Kuipers, Jack
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is...
Semiclassical gaps in the density of states of chaotic Andreev billiards (2009)
Kuipers, Jack, Waltner, Daniel, Petitjean, Cyril, Berkolaiko, Gregory, Richter, Klaus
The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an...
A lower bound for nodal count on discrete and metric graphs (2006)
According to a well-know theorem by Sturm, a vibrating string is divided into exactly N nodal intervals by zeros of its N-th eigenfunction. Courant showed that one half of Sturm's theorem for the...
Form factor expansion for large graphs: a diagrammatic approach (2006)
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a...
Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equation (2005)
Berkolaiko, Gregory, Rodkina, Alexandra
We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial...
Star graphs and Seba billiards (2005)
Berkolaiko, Gregory, Bogomolny, Eugene, Keating, J.P.
We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding...
Multiplicity of periodic solutions in bistable equations (2003)
Berkolaiko, Gregory, Grinfeld, Michael
We study the number of periodic solutions in two first order non-autonomous differential equations both of which have been used to describe, among other things, the mean magnetization of an Ising...
Form factor for a family of quantum graphs: An expansion to third order (2002)
Berkolaiko, Gregory, Schanz, Holger, Whitney, Robert S.
For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the...
The Leading Off-Diagonal Correction to the Form Factor of Large Graphs (2001)
Berkolaiko, Gregory, Schanz, Holger, Whitney, Robert S.
Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, $K(\tau)$, of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We...
Star graphs and Seba billiards (2001)
Berkolaiko, Gregory, Bogomolny, Eugene, Keating, J.P.
We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding...
Star graphs and Seba billiards (2001)
Berkolaiko, Gregory, Bogomolny, Eugene, Keating, J.P.
We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding...
Quantum star graphs and related systems. (2000)
Thesis (Ph. D.)--University of Bristol, 2000.