Abstract
We demonstrate the application of transition state theory to wave packet dynamics in metastable Schrödinger systems which are approached by means of a variational ansatz for the wavefunction and whose dynamics is described within the framework of a time-dependent variational principle. The application of classical transition state theory, which requires knowledge of a classical Hamilton function, is made possible by mapping the variational parameters to classical phase space coordinates and constructing an appropriate Hamiltonian in action variables. This mapping, which is performed by a normal form expansion of the equations of motion and an additional adaptation to the energy functional, as well as the requirements to the variational ansatz are discussed in detail. The applicability of the procedure is demonstrated for a cubic model potential for which we calculate thermal decay rates of a frozen Gaussian wavefunction. The decay rate obtained with a narrow trial wavefunction agrees perfectly with the results using the classical normal form of the corresponding point particle. The results with a broader trial wavefunction go even beyond the classical approach, i.e. they agree with those using the quantum normal form. The method presented here will be applied to Bose–Einstein condensates in the following paper (Junginger et al 2012 J. Phys. A: Math. Theor. 45 155202).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.