Chaotic transport close to regular structures in 4D symplectic maps

• Applicant: Professor Dr. Roland Ketzmerick
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 290128388

Higher-dimensional Hamiltonian systems occur in many areas of physics, chemistry, and mathematics. Their understanding is the key to, e.g., predict the stability of celestial motion, control the beams of particle accelerators, and to describe chemical reactions. We will concentrate on Hamiltonian systems with three degrees of freedom, which is the lowest dimensional case where chaotic transport can circumvent regular tori. Such systems can be reduced to 4D symplectic maps. Generically they are far from integrability with regular and chaotic dynamics coexisting in the 4D phase space. In the second funding period we want to focus on (A) classical and (B) quantum aspects: (A) We will study partial transport barriers in chaotic regions. In 4D maps it is an open problem which objects in phase space limit chaotic transport, which are most relevant, and how to compute the flux across such partial barriers. (B) We will study new quantum signatures of chaotic transport that emerge due to the phase-space structure in higher-dimensional Hamiltonian systems.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Arnd Bäcker