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Extreme values of CUE characteristic polynomials: a numerical study (2018)
Journal Article
Fyodorov, Y. V., Gnutzmann, S., & Keating, J. P. (2018). Extreme values of CUE characteristic polynomials: a numerical study. Journal of Physics A: Mathematical and Theoretical, 51(46), doi:10.1088/1751-8121/aae65a

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

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops (2017)
Journal Article
Fan, Y., Gnutzmann, S., & Liang, Y. (in press). Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops. Physical Review E, 96(6), doi:10.1103/PhysRevE.96.062207. ISSN 2470-0045

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

Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures (2016)
Journal Article
Gnutzmann, S., & Waltner, D. (in press). Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures. Physical Review E, 94(6), doi:10.1103/PhysRevE.94.062216. ISSN 2470-0045

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

Quantum walks and quantum search on graphene lattices (2015)
Journal Article
Foulger, I., Gnutzmann, S., & Tanner, G. (2015). Quantum walks and quantum search on graphene lattices. Physical Review A, 91(6), doi:10.1103/PhysRevA.91.062323. ISSN 2469-9926

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

Microwave experiments simulating quantum search and directed transport in artificial graphene (2015)
Journal Article
Böhm, J., Bellec, M., Mortessagne, F., Kuhl, U., Barkhofen, S., Gehler, S., …Tanner, G. (2015). Microwave experiments simulating quantum search and directed transport in artificial graphene. Physical Review Letters, 114(11), doi:10.1103/PhysRevLett.114.110501. ISSN 0031-9007

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