Transition state theory for wave packet dynamics: I. Thermal decay in metastable Schrödinger systems

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 applicati...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-04, Vol.45 (15), p.155201-18
Main Authors: Junginger, Andrej, Main, Jörg, Wunner, Günter, Dorwarth, Markus
Format: Article
Language:English
Subjects:
Bose-Einstein condensate
Decay rate
Dynamical systems
Dynamics
Exact sciences and technology
Gaussian wavefunction
Mapping
Mathematical analysis
Mathematical models
metastable Schroedinger system
normal form
Physics
Schroedinger equation
thermal decay
transition state theory
wave packet
Wave packets
Wavefunctions
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Summary: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).
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/15/155201