Classical and quantum dynamics of time-dependent billiards

• Antragsteller: Professor Dr. Peter Schmelcher
• Fachliche Zuordnung: Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik
• Förderung: Förderung von 2007 bis 2011
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 48246955

• Erstellungsjahr: 2012

Zusammenfassung der Projektergebnisse

In this project on the classical and quantum dynamics of time-driven billiards major progress has been achieved with respect to the fundamental understanding of dynamical mechanisms in this open non-conservative systems. On the side of the escape rates out of the breathing billiard it has been shown that the decay rate of the remaining particles is closely connected to the decomposition of the phase space in the billiard and to the existence of exact or approximate constants of motion. The dependence of the emission rate of the parameters of the driving has been analyzed and the tunability of it has been demonstrated. Fermi acceleration has become one of the focus issues in this project. We have achieved substantial progress in the understanding of the occurence of Fermi acceleration, depending on the type of billiard and in particular its driving law. An intriguing mechanism in the time evolution has been identified: For short times the mixed phase space provides us with an anomalous diffusion in momentum space whereas with increasing time the chaotic part of phase space is squeezed into a narrow channel around the separatrix which yields normal diffusion and therefore normal Fermi acceleration. Combining the above with frictional forces it has been shown that a device can be constructed that creates out of a uniform homogeneous particle distribution (at finite temperature) a monochromatic narrowly focused beam just because periodic orbits form attractors in phase space onto which the dynamics can be directed. The quantum dynamics of the project has been shown to be very rich in excitation and energy transfer processes. A detailed understanding and modeling of the ab initio quantum dynamical results have been achieved and performed. A Rabi-like N-state model could explain part of the energy transfer processes and was augmented by perturbation theoretical treatment that finally explained the complex dynamics.

Projektbezogene Publikationen (Auswahl)

• Scattering Dynamics of Driven Closed Billiards. Europhysics Letters 79, 20002 (2007)
  F. Lenz, F. K. Diakonos and P. Schmelcher
  
• Tunable Fermi Acceleration in the Driven Elliptical Billiard. Physical Review Letters 100, 014103 (2008)
  F. Lenz, F. K. Diakonos and P. Schmelcher
  
• Evolutionary Phase Space in Driven Elliptical Billiards. New Journal of Physics 11, 083035 (2009)
  F. Lenz, C. Petri, F. R. N. Koch, F. K. Diakonos and P. Schmelcher
  
• Particle Focusing in Oscillating Dissipative Billiards. Physical Review E (R) 82, 035204 (2010)
  C. Petri, F. Lenz, F.K. Diakonos and P. Schmelcher
  
• Phase Space Interpretation of Exponential Fermi Acceleration. New Journal of Physics 13, 093039 (2011)
  B. Liebchen, R. Büchner, C. Petri, F.K. Diakonos, F. Lenz and P. Schmelcher
  
• Resonant Population Transfer of the Time-Dependent Quantum Elliptical Billiard. New Journal of Physics 13, 103019 (2011)
  F. Lenz, B. Liebchen, F.K. Diakonos and P. Schmelcher