Scattering signatures of systems with a mixed phase space
Zusammenfassung der Projektergebnisse
Hamiltonian systems typically show a mixed phase space with both regular and chaotic dynamics. These properties of the classical dynamics are reflected in the more fundamental quantum mechanical description. In addition to the rather well understood quantum properties of completely regular and fully chaotic systems, novel phenomena arise from the coexistence of regular and chaotic dynamics and have been investigated for closed and scattering systems. Our main focus was on scattering and tunneling in systems with a mixed phase space. In particular, we developed a semiclassical complex path approach for dynamical tunneling rates, describing the transition from a regular island to the chaotic phase-space component. This was based on the fictitious integrable system approach established in the first funding period. Furthermore, we were able to show that regular-to-chaotic tunneling leads to fractional power-law level spacing distributions. The phenomenon of resonance-assisted tunneling has been studied theoretically and in an experimental collaboration. In another experimental collaboration we helped with the planning and interpretation of cold atom experiments demonstrating the Poincaré-Birkhoff scenario in a periodically driven system. A second focus were systems with more than two degrees of freedom. In such higher dimensional systems regular tori do not separate regions in phase space. Therefore one has no longer regular islands but complicated regular phase-space structures penetrated by chaotic motion. We proposed a new method which allows for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. Quantum mechanically, this gives the first comparison of Husimi functions of eigenstates of 4D maps with classical phase-space structures, confirming the semi-classical eigenfunction hypothesis. Beyond the original plans for the project we established the universal scaling properties of the quantum localization–delocalization transition due to the presence of partial transport barriers, which are ubiquitous in chaotic phase-space regions. We also derived a partial Weyl law, which counts the number of eigenstates in a billiard corresponding to an invariant subregion of phase space. Furthermore, we found a surprising generalization of Bose-Einstein condensation to time-periodic systems or more generally to non-equilibrium steady states. We find the unambiguous selection of an odd number of states acquiring large occupations and derive a criterion for when a single and when multiple states are Bose selected in a non-interacting gas. We propose a quantum switch for heat conductivity based on shifting between one and three selected states. This work received the label editors suggestion and was featured in a focus article.
Projektbezogene Publikationen (Auswahl)
- Regular-to-chaotic tunneling rates: From the quantum to the semiclassical regime, Phys. Rev. Lett. 104, 114101 (2010)
S. Löck, A. Bäcker, R. Ketzmerick, and P. Schlagheck
(Siehe online unter https://doi.org/10.1103/PhysRevLett.104.114101) - Fractional-Power-Law Level Statistics Due to Dynamical Tunneling, Phys. Rev. Lett. 106, 024101 (2011)
A. Bäcker, R. Ketzmerick, S. Löck, and N. Mertig
(Siehe online unter https://doi.org/10.1103/PhysRevLett.106.024101) - Partial Weyl law for billiards, Europhys. Lett. 94, 30004 (2011)
A. Bäcker, R. Ketzmerick, S. Löck, and H. Schanz
(Siehe online unter https://doi.org/10.1209/0295-5075/94/30004) - Universal quantum localizing transition of a partial barrier in a chaotic sea, Phys. Rev. Lett. 109, 234101 (2012)
M. Michler, A. Bäcker, R. Ketzmerick, H.-J. Stöckmann, and S. Tomsovic
(Siehe online unter https://doi.org/10.1103/PhysRevLett.109.234101) - Complex paths for regular-to-chaotic tunnelling rates, Europhys. Lett. 102, 10005 (2013)
N. Mertig, S. Löck, A. Backer, R. Ketzmerick, and A. Shudo
(Siehe online unter https://doi.org/10.1209/0295-5075/102/10005) - Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems, Phys. Rev. Lett. 111,240405 (2013)
D. Vorberg, W Wustmann, R. Ketzmerick, and A. Eckardt
(Siehe online unter https://doi.org/10.1103/PhysRevLett.111.240405) - Hierarchical fractal Weyl laws for chaotic resonance states in open mixed systems, Phys. Rev. Lett. 111, 114102 (2013)
M. J. Körber, M. Michler, A. Bäcker, and R. Ketzmerick
(Siehe online unter https://doi.org/10.1103/PhysRevLett.111.114102) - Visualization and comparison of classical structures and quantum states of 4D maps, Phys. Rev. E. 89, 022902 (2014)
M. Richter, S. Lange, A. Bäcker, and R. Ketzmerick
(Siehe online unter https://doi.org/10.1103/PhysRevE.89.022902)
