Decoherence in the photosynthesis process
Université Paul Sabatier
Slides of the talk
Classical theories are sometimes inappropriate to describe very efficient biological processes in nature, which seem to be better understood via quantum mechanics. However, we are still far from understanding how quantum features can survive in open quantum systems. In this talk, I would like to present a mathematical model and some numerical simulations for the illustration of the excitation energy transfer in photosynthesis complexes, with the aim to study the environmental induced decoherence effect. The model is based on the Schrödinger equation, describing the propagation of an absorbed excitation (photon) through a spin-chain towards the photosynthesis reaction center, and this in continuous interaction with a vibrational environment (phonon).
Emergence of Haldane pseudo-potentials in systems with short range interactions
University of Vienna
Slides of the talk
In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane's pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of a hard core. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level. This is joint work with Robert Seiringer.