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How to find us prof. dr. H. (Holger) Waalkens

Research interests

My research is in the fields of dynamical systems theory and semiclassical quantum mechanics (short wavelengths asymptotics). My research is very broad and applied in nature and a general guiding principle is to make an impact on prominent problems in the natural sciences (mainly atomic and molecular physics, celestial mechanics, electron transport problems and optics). In fact I strongly believe that in order to be successful in modern science one cannot afford to have borders between different disciplines. My interest in dynamical systems first of all concerns Hamiltonian systems and has a very geometric flavor. This also relates to semiclassical quantum mechanics which provides techniques to relate quantum states (their wave functions or phase space analogues like Wigner or Husimi functions) to classical phase space structures in the limit where Planck's constant can be considered as small compared to other characteristic scales of the quantum problem (this could, e.g., mean that the quantum mechanical wavelength is short compared to classical lengths scales). This does not only shed light on the quantum problem as such but also provides powerful techniques to compute quantities which are notoriously difficult to compute from ab initio quantum calculations.

More information on my personal pages.

Publications

Chaotic dynamics from a pseudo-linear system

Dynamics Associated with the Normally Hyperbolic Invariant Manifold that Governs the Ionization of Hydrogen in a Circularly Polarized Electric Field

Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction

A Lagrangian Fibration of the Isotropic 3-Dimensional Harmonic Oscillator with Monodromy

Comment on ’Winding around non-Hermitian singularities’ by Zhong et al., Nat. Commun. 9, 4808 (2018)

Critical points of the integral map of the charged 3-body problem

Scattering invariants in Euler’s two-center problem

Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator

Defect in the Joint Spectrum of Hydrogen due to Monodromy

Dependence of chaotic actuation dynamics of Casimir oscillators on optical properties and electrostatic effects

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