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DY: Fachverband Dynamik und Statistische Physik
DY 52: Quantum Dynamics, Decoherence and Quantum Information
DY 52.9: Vortrag
Donnerstag, 19. März 2020, 17:15–17:30, HÜL 186
The Periodical Driven, Anharmonic Oscillator — Mattes Heerwagen and •Andreas Engel — Carl von Ossietzky Universität, Oldenburg, Germany
In the thermodynamics of nanoscopic systems the correspondence between classical and quantum mechanical description is of particular importance. To scrutinize this relationship we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics.
More precisely, we are interested in the energy change of the oscillator induced by the external drive. It is closely related to the distribution of work in the system. Since the amplitude λ(t) of the external drive increase from zero to a maximum λmax and than decrease back to zero initial and final Hamiltonian coincide. Our main quantity of interest is the probability density P(Ef|Ei) for transitions from initial energy Ei to final energy Ef.
In the classical case non-diagonal transitions with Ef≠ Ei mainly arise due to the mechanism of separatrix crossing. It is most efficiently analyzed using action-angle variables. Within the pendulum approximation analytical results for the transition probability can then be compared with numerical simulations. In the quantum case numerically exact results are complemented with analytical arguments employing Floquet techniques. The latter highlight in particular the mechanism behind the periodical variation of P(Ef|Ei) with the maximal amplitude λmax of the drive.