No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
A two-layer approach to the coupled coherent states method
2.C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis, Zurich Lectures in Advanced Mathematics (European Mathematical Society (EMS), 2008).
31.G. D. Billing, The Quantum Classical Theory (Oxford University Press, Oxford, NY, 2003).
32.J. R. Klauder and B. S. Skagerstam, Coherent States: Applications in Physics and Mathematical Physics (World Scientific, Singapore, 1985).
41.P. Kramer and M. Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, Heidelberg, 1981).
42. We assume real parameters for simplicity, but, of course, this also accounts for complex parametrisations: One can always work separately with real and imaginary parts or, alternatively, treat the parameters and their complex conjugates as independent variabless – both approaches are equivalent.
43. In order to come to this conclusion one must consider the case of unrestricted variations and work out the Euler-Lagrange equations of motion; the resulting equation coincides with the Schrödinger equation except for a time-dependent phase; both normalisation factor and action phase are introduced precisely to cancel this factor.
44. The coefficients bkn in Eq. (A7) differ from the coefficients akn of Eq. (8) by a time-dependent phase – see Eq. (14).
Article metrics loading...
In this paper, a two-layer scheme is outlined for the coupled coherent states(CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, matching-pursuit/split-operator Fourier transform, and configuration interaction expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations.
Full text loading...
Most read this month