First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy

Westermann T, Manthe U (2012)
The Journal of Chemical Physics 136(20).

Journal Article | Published | English

No fulltext has been uploaded

Abstract
A new concept to describe the quantum dynamics in complex systems is suggested. It extends established schemes based on the Dirac-Frenkel variation principle, e.g., the multi-configurational time-dependent Hartree (MCTDH) approach. The concept is based on a correlation-based von Neumann entropy (CvN-entropy) definition measuring the complexity of the wavefunction. Equations of motion are derived using a CvN-entropy constraint in the variational principle and result in a generally applicable effective Hamiltonian. It consists of the standard Hamilton operator and an additional nonlinear operator which limits the complexity of the wavefunction. Effectively, this nonlinear operator absorbs complex structures which are emerging in the wavefunction and allows one to introduce non-norm conserving equations of motion. Important aspects of the new concept are outlined studying the wave packet propagation on the diabatic B-2 potential energy surfaces of NO2. First, it is demonstrated that during standard wave packet propagation the CvN-entropy increases strongly with time roughly independent of the coordinate systems employed. Second, one finds that employing CvN-entropy constrained MCTDH propagation yields improved wave function accuracy on longer time scales while compromising on the short time accuracy. Third, the loss of the wave-function's norm is directly related to the overlap with the exact wavefunction. This provides an error estimate available without knowing an exact reference. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720567]
Publishing Year
ISSN
PUB-ID

Cite this

Westermann T, Manthe U. First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy. The Journal of Chemical Physics. 2012;136(20).
Westermann, T., & Manthe, U. (2012). First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy. The Journal of Chemical Physics, 136(20).
Westermann, T., and Manthe, U. (2012). First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy. The Journal of Chemical Physics 136.
Westermann, T., & Manthe, U., 2012. First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy. The Journal of Chemical Physics, 136(20).
T. Westermann and U. Manthe, “First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy”, The Journal of Chemical Physics, vol. 136, 2012.
Westermann, T., Manthe, U.: First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy. The Journal of Chemical Physics. 136, (2012).
Westermann, Till, and Manthe, Uwe. “First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy”. The Journal of Chemical Physics 136.20 (2012).
This data publication is cited in the following publications:
This publication cites the following data publications:

2 Citations in Europe PMC

Data provided by Europe PubMed Central.

Electron-vibration entanglement in the Born-Oppenheimer description of chemical reactions and spectroscopy.
McKemmish LK, McKenzie RH, Hush NS, Reimers JR., Phys Chem Chem Phys 17(38), 2015
PMID: 26204101

49 References

Data provided by Europe PubMed Central.


AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0
Effect of classical bifurcations on the quantum entanglement of two coupled quartic oscillators.
Santhanam MS, Sheorey VB, Lakshminarayan A., Phys Rev E Stat Nonlin Soft Matter Phys 77(2 Pt 2), 2008
PMID: 18352109

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0
Material in PUB:
Part of this Dissertation

Export

0 Marked Publications

Open Data PUB

Web of Science

View record in Web of Science®

Sources

PMID: 22667549
PubMed | Europe PMC

Search this title in

Google Scholar