Coherent transport of waves in disordered systems with nonlinearity and interactions
Final Report Abstract
The aim of the present project has been to investigate the interplay between disorder and nonlinearity (or interactions) in the propagation of waves (or quantum particles) through random media. A crucial question for understanding how waves (e.g. light waves) propagate in random media (e.g. clouds consisting of small water droplets) is to what extent the phenomenon of wave interference affects the diffusive propagation of the wave. In general (for not too strongly scattering media in three dimensions), interference can be shown to lead to an enhancement of the intensity scattered in exact backwards direction (coherent backscattering) and, closely related to that, a reduction of diffusion (weak localization). In one part of the present project, we investigated scattering of atomic matter waves by a random potential. In addition to the above mentioned effects due to interference, propagation is now also affected by interactions between the particles (which typically repel each other). We developed a microscopic scattering theory in order to analyze the resulting interplay between disorder and interactions. In particular, our theory also includes inelastic collisions between the atoms (where energy is transferred between two atoms) – which is not taken into account in previous works analyzing the same scenario under the assumption that all atoms are described by the same wavefunction (mean field approximation). In contrast, we showed that, even at weak interaction strenghts, inelastic collisions do have a pronounced impact on the transport behaviour: they lead to an efficient thermalization of the single-particle energies and slow down the decrease of the coherent backscattering interference with increasing interaction strength as compared to the purely elastic case described by the mean field approximation. In another project part, we worked on the theoretical description of the weak localization effect – and its relation to coherent backscattering – in the linear regime which turned out to be less well understood than originally expected. We have been able to clarify some fundamental aspects of weak localization for linear scattering media which have been unknown so far. In particular, we calculated the interference corrections of the transport and the scattering mean free path for weak disorder (which, in some respect, deviate from standard textbook results) and identified those weak localization diagrams which, in the presence of a boundary surface, restore flux conservation in coherent backscattering of light. The remaining parts of the project include an analysis of the formation of instabilities in nonlinear disordered scattering media and several other aspects of propagation of quantum particles or waves in random media.
Publications
- Entanglement and Thouless times from coincidence measurements across disordered media, Phys. Rev. A 83, 033827 (2011)
N. Cherroret, A. Buchleitner
- Fokker-Planck equation for transport of wave packets in nonlinear disordered media, Phys. Rev. E 84, 021114 (2011)
N. Cherroret, T. Wellens
- Bunching and anti-bunching of localised particles in disordered media, Europhys. Lett. 99, 14001 (2012)
F. Schlawin, N. Cherroret, A. Buchleitner
(See online at https://doi.org/10.1209/0295-5075/99/14001) - Controlled engineering of extended states in disordered systems, Phys. Rev. B 86, 085119 (2012)
A. Rodriguez, A. Chakrabarty, R.A. Römer
(See online at https://doi.org/10.1103/PhysRevB.86.085119) - Inelastic multiple scattering of interacting bosons in weak random potentials, Phys. Rev. Lett. 109, 030601 (2012)
T. Geiger, T. Wellens, A. Buchleitner
(See online at https://doi.org/10.1103/PhysRevLett.109.030601) - Nonlinear reciprocity breaking through ultrafast dynamics in a random photonic medium, Phys. Rev. Lett. 108, 223906 (2012)
O.L. Muskens, P. Venn, T. van der Beek, T. Wellens
(See online at https://doi.org/10.1103/PhysRevLett.108.223906) - Weak disorder corrections of the scattering and transport mean free path, J. Phys. A 45, 395101 (2012)
F. Eckert, A. Buchleitner, T. Wellens
(See online at https://doi.org/10.1088/1751-8113/45/39/395101) - Flux conservation in coherent backscattering and weak localisation of light, J. Phys. A 46, 315101 (2013)
A. Knothe, T. Wellens
- Microscopic scattering theory for interacting bosons in weak random potentials, New J. Phys. 15, 115015 (2013)
T. Geiger, A. Buchleitner, T. Wellens
(See online at https://doi.org/10.1088/1367-2630/15/11/115015)
