Nonsingular constraints in time-dependent variational principle for parametrized wave functions
K. Ohta. International Journal of Quantum Chemistry, 113 (2):
161--170(January 2013)
DOI: 10.1002/qua.24325
Abstract
In this work, we consider two conditions required for the nonsingularity of constraints in the time-dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second-class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP-parameters, the regularity and the second-class conditions become equivalent. The second-class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second-class condition in an extended canonical phase-space.
%0 Journal Article
%1 QUA:QUA24325
%A Ohta, Katsuhisa
%D 2013
%I Wiley Subscription Services, Inc., A Wiley Company
%J International Journal of Quantum Chemistry
%K constraint mechanics physics quantum variational
%N 2
%P 161--170
%R 10.1002/qua.24325
%T Nonsingular constraints in time-dependent variational principle for parametrized wave functions
%U http://dx.doi.org/10.1002/qua.24325
%V 113
%X In this work, we consider two conditions required for the nonsingularity of constraints in the time-dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second-class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP-parameters, the regularity and the second-class conditions become equivalent. The second-class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second-class condition in an extended canonical phase-space.
@article{QUA:QUA24325,
abstract = {In this work, we consider two conditions required for the nonsingularity of constraints in the time-dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second-class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP-parameters, the regularity and the second-class conditions become equivalent. The second-class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second-class condition in an extended canonical phase-space.},
added-at = {2012-12-26T06:24:28.000+0100},
author = {Ohta, Katsuhisa},
biburl = {https://www.bibsonomy.org/bibtex/2150bbc42f77019f094cd42f1e57ddfab/drmatusek},
doi = {10.1002/qua.24325},
interhash = {4456a1f731225b4f0032a5e7349fa4c1},
intrahash = {150bbc42f77019f094cd42f1e57ddfab},
issn = {1097-461X},
journal = {International Journal of Quantum Chemistry},
keywords = {constraint mechanics physics quantum variational},
month = jan,
number = 2,
pages = {161--170},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
timestamp = {2013-03-01T03:12:41.000+0100},
title = {Nonsingular constraints in time-dependent variational principle for parametrized wave functions},
url = {http://dx.doi.org/10.1002/qua.24325},
volume = 113,
year = 2013
}