Nonlinear transport of bosonic matter waves and light
Final Report Abstract
The region where both complex single-particle dynamics and many-body interactions play an important role is a natural place to apply semiclassical techniques. In this report, we have presented several instances where novel and robust quantum effects characterisric of this regime can be theoretically addressed using semiclassical approaches. The work within P8 has been, up to certain point, exhaustive in the sense of describing different types of complex quantum systems by using all the posibilities given by the semiclassical approach. Coherent effects within the framework of discrete cold-atom systems, as realized by the Bose-Hubbard hamiltonian, are studied in terms of classical paths and their interference in an abstract high dimensional space of occupation numbers. A new physical effect (coherent back scattering in Fock space) is universally predicted and fully conformed by numerical simulations. At the level of the mean field approach, the short wavenumber limit of the continuos Gross-Pitaevskii equation can be studied in terms of classical paths in real space, together with a diagramatic approach to include interactions perturbatively. Again, good agreement between the universal predictions of the theory and numerical calculations is found. In particular, for the coherent reduction of the weak localization peak in the transmission of cold atoms through chaotic cavities. Finally, the recently propossed expansion of the smooth many-body density of states for confined systems has been shown to describe very well the behavior of the many-body spectrum for noninteracting systems in the whole regime of energies. This is a genuine quantum mechanical approach, most suitable for situations where the field-theoretical description runs into technical problems due to the orbital degrees of freedom.
Publications
- Conductance and thermopower of ballistic Andreev cavities, Phys. Rev. B 83, 205414 (2011)
T. Engel, J. Kuipers, and K. Richter
(See online at https://doi.org/10.1103/PhysRevB.83.205414) - Fidelity decay for local perturbations: Microwave evidence for oscillating decay exponents, Phys. Rev. E 83, 016214 (2011)
B. Köber, U. Kuhl, H.-J. Stöckmann, A. Goussev, and K. Richter
(See online at https://doi.org/10.1103/PhysRevE.83.016214) - Delocalization of ultracold atoms in a disordered potential due to light scattering, Phys. Rev. A 86, 043610 (2012)
B. Nowak, J. J. Kinnunen, M. J. Holland, and P. Schlagheck
(See online at https://doi.org/10.1103/PhysRevA.86.043610) - Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories, Phys. Rev. E 85, 045201 (2012)
G. Berkolaiko and J. Kuipers
(See online at https://doi.org/10.1103/PhysRevE.85.045201) - Weak localization with nonlinear bosonic matter waves, Ann. Phys. 327, 1998 (2012)
T. Hartmann, J. Michl, C. Petitjean, T. Wellens, J.-D. Urbina, K. Richter, and P. Schlagheck
(See online at https://doi.org/10.1016/j.aop.2012.04.002) - Random quantum states: recent developments and applications, Adv. in Phys. 62, 363 (2013)
J. D. Urbina and K. Richter
(See online at https://doi.org/10.1080/00018732.2013.860277) - Universal spatial correlations in spinor random fields, Phys. Rev. E 87, 042115 (2013)
J. D. Urbina, M. Wimmer, D. Bauernfeind, D. Espitia, I. Adagideli, and K. Richter
(See online at https://doi.org/10.1103/PhysRevE.87.042115) - Coherent Backscattering in Fock Space: a Signature of Quantum Many-Body Interference in Interacting Bosonic Systems, Phys. Rev. Lett. 112, 140403 (2014)
T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina
(See online at https://doi.org/10.1103/PhysRevLett.112.140403) - The Weyl expansion for systems of independent identical particles, J. Phys. A: Math. Theor. 47, 015101 (2014)
Q. Hummel, J. D. Urbina, and K. Richter
(See online at https://doi.org/10.1088/1751-8113/47/1/015101)
