All Outputs (13)

Closed form expressions for the Green’s function of a quantum graph—a scattering approach (2023)
Journal Article

In this work we present a three step procedure for generating a closed form expression of the Green’s function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the approach... Read More about Closed form expressions for the Green’s function of a quantum graph—a scattering approach.

A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs (2022)
Journal Article

We generalize the scattering approach to quantum graphs to quantum graphs with piecewise constant potentials and multiple excitation modes. The free single-mode case is well-known and leads to the trace formulas of Roth (1983 C. R. Acad. Sci., Paris... Read More about A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs.

On the nodal structure of nonlinear stationary waves on star graphs (2019)
Journal Article

We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schrödinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that... Read More about On the nodal structure of nonlinear stationary waves on star graphs.

Extreme values of CUE characteristic polynomials: a numerical study (2018)
Journal Article

We present the results of systematic numerical computations relating to the extreme value statistics of the characteristic polynomials of random unitary matrices drawn from the circular unitary ensemble (CUE) of random matrix theory. In particular, w... Read More about Extreme values of CUE characteristic polynomials: a numerical study.

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops (2017)
Journal Article

We consider two coupled quantum tops with angular momentum vectors L and M. The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the... Read More about Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops.

Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures (2016)
Journal Article

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in o... Read More about Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures.

Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory (2016)
Journal Article

Electron-hole coherent states for the Bogoliubov-de Gennes equation (2016)
Journal Article

A review of sigma models for quantum chaotic dynamics (2015)
Journal Article

Quantum walks and quantum search on graphene lattices (2015)
Journal Article

Quantum walks have been very useful in developing search algorithms in quantum information, in particular for devising of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in two-dimensional lattices ha... Read More about Quantum walks and quantum search on graphene lattices.

Microwave experiments simulating quantum search and directed transport in artificial graphene (2015)
Journal Article

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to \sqrt{N}, where N is the number of items in the search space. In particular, devising searches on regul... Read More about Microwave experiments simulating quantum search and directed transport in artificial graphene.

Quantum search on graphene lattices (2014)
Journal Article

We present a continuous-time quantum search algorithm on a graphene lattice. This provides the sought- after implementation of an efficient continuous-time quantum search on a two-dimensional lattice. The search uses the linearity of the dispersion r... Read More about Quantum search on graphene lattices.

Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs (2013)
Journal Article

We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the cancellation of long... Read More about Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs.