Non Hermitian dynamics of disordered media and interacting atomic Bose-Einstein Condensates
Final Report Abstract
The scope of this project has extended over several aspects of wave dynamics in random and complex media in open, active and non-equilibrium systems, and it has lead to a number of very interesting as documented by the range of publications. Extreme and rare events have in recent years started to draw more and more interest in various fields of science. In wave propagation theses extreme events are often called rogue or freak waves, whose origin in natural systems - e.g. in wind driven ocean waves - are still widely disputed. Some theories study the role of nonlinearities in the wave equations but more recently it has become clear that already linear wave dynamics in correlated random media very generically leads to strong fluctuations and freak waves, a phenomenon called branching. Within this project we have strongly contributed to the statistical theory of these branched flows and their dependencies on the properties of the medium. Among the results is e.g. a joint work with P1 that for the first time showed the scaling of the branch structures in experiment and our most recent work that gives an analytical expression for the distribution of highest waves and confirmed it by extensive numerical calculations. The realization of optical systems with exactly balanced gain and loss domains open new possibilities in photonics. These systems are characterized by a complex index of refraction with the property n(x) = n∗(−x) and are described by phenomenological Hamiltonians which commute with the joint parity-time PT operator. We have proposed architectures of waveguide arrays with robust PT-symmetry that provide high control of light propagation and investigated the beam dynamics generated by these structures. Among our achievements are unidirectional light propagation, conical diffraction with high values of group velocities, and reconfigurable Talbot effects. In a further activity we studied the possibility that generic wave excitations show self-trapping, i.e. localization due to the presence of nonlinearities and discreteness, in Bose-Einstein-condensates in optical lattices. We have shown theoretically and numerically how the transitions to self-trapping can occur for initially extended excitations. We have also investigated the effects of quantum correlations and fluctuations in BEC’s in the presence of optical lattices. The simplest mathematical model that allows for such investigations is the so-called dimeric Bose-Hubbard Hamiltonian (BHH). For such system (in the so-called Josephson regime) we have found using semi-classical analysis that there is a universal value for the builtup of coherence between two initially separated condensates. Along the same lines, we have devised a microscopic scattering approach that allowed us to probe the excitation spectrum of a BEC. The proposed methodology was employing both semiclassical and using Random Matrix Theory considerations, in order to analyze the scattering cross section of an inelastically scattered test particle from a BEC. Finally we have investigated thermal transport in complex networks of coupled harmonic oscillators with random spring constants. Using a variant of Random Matrix Theory we have found that such systems show anomalous mesoscopic fluctuations which are associated with strong correlations between the normal modes of the system. For quasi-one dimensional geometries we have developed a renormalization theory for the calculation of the heat current which allowed us to conclude that Fourier law is violated in such systems.
Publications
- Optical structures with local PT-symmetry, J. Phys. A 43, 265305 (2010)
O. Bendix, R. Fleischmann, T. Kottos, B. Shapiro
(See online at https://doi.org/10.1088/1751-8113/43/26/265305) - Universal Statistics of Branched Flows, Phys. Rev. Lett. 105, 020601 (2010)
J. J. Metzger, R. Fleischmann, and T. Geisel
(See online at https://doi.org/10.1103/PhysRevLett.105.020601) - Matter-wave scattering on a BEC in a double-well potential, European Physical Journal D 63, 55 (2011)
S. Hunn, M. Hiller, A. Buchleitner, D. Cohen, T. Kottos
(See online at https://doi.org/10.1140/epjd/e2011-10639-9) - Inelastic chaotic scattering on a Bose-Einstein condensate, J. Phys. B 45, 085302 (2012)
S. Hunn, M. Hiller, D. Cohen, T. Kottos, A. Buchleitner
(See online at https://doi.org/10.1088/0953-4075/45/8/085302) - PT-Symmetric Talbot Effects, Phys. Rev. Lett. 109, 033902 (2012)
H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos
(See online at https://doi.org/10.1103/PhysRevLett.109.033902) - Experimental Observation of a Fundamental Length Scale of Waves in Random Media, Phys. Rev. Lett. 111, 183902 (2013)
S. Barkhofen, J. J. Metzger, R. Fleischmann, U. Kuhl, and H.-J. Stöckmann
(See online at https://doi.org/10.1103/PhysRevLett.111.183902) - Intensity Fluctuations of Waves in Random Media: What Is the Semiclassical Limit? Phys. Rev. Lett. 111, 013901 (2013)
J. J. Metzger, R. Fleischmann, and T. Geisel
(See online at https://doi.org/10.1103/PhysRevLett.111.013901) - Nature of self-localization of Bose-Einstein condensates in optical lattices, Phys. Rev. A 87, 033605 (2013)
H. Hennig and R. Fleischmann
(See online at https://doi.org/10.1103/PhysRevA.87.033605) - Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains, Phys. Rev. E 87, 020101 (2013)
J. D. Bodyfelt, M. C. Zheng, R. Fleischmann, T. Kottos
(See online at https://doi.org/10.1103/PhysRevE.87.020101)
