2003
DOI: 10.1063/1.1625366
|View full text |Cite
|
Sign up to set email alerts
|

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Abstract: Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first-and second-order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite a… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

7
101
0

Year Published

2005
2005
2019
2019

Publication Types

Select...
7
1

Relationship

3
5

Authors

Journals

citations
Cited by 62 publications
(108 citation statements)
references
References 39 publications
7
101
0
Order By: Relevance
“…22 for several types of constraints. These estimators are derived in a similar manner, based on the rescaling of coordinates and a finite difference evaluation of the derivative with respect to β that was used for the first time by Predescu and coworkers for reactant energies and heat capacities [27]. The statistical error of these estimators showed a surprising behavior in comparison with the estimators for E r .…”
Section: E Temperature Dependence Of the Rate Constantmentioning
confidence: 99%
“…22 for several types of constraints. These estimators are derived in a similar manner, based on the rescaling of coordinates and a finite difference evaluation of the derivative with respect to β that was used for the first time by Predescu and coworkers for reactant energies and heat capacities [27]. The statistical error of these estimators showed a surprising behavior in comparison with the estimators for E r .…”
Section: E Temperature Dependence Of the Rate Constantmentioning
confidence: 99%
“…Therefore, the thermodynamic estimators obtained from formal differentiation against the inverse temperature have finite variance in the limit of large number of path variables [13,32,33]. As for random series, Eq.…”
Section: B Sampling Efficiency For the Normal Mode Approach To Lie-tmentioning
confidence: 99%
“…(48). The estimators have been reviewed elsewhere [32,33]. In the case where all path variables are updated simultaneously, we have employed the same maximal displacements for all variables a l,j and b l,j .…”
Section: An Application Of the Lévy-ciesielski Implementationmentioning
confidence: 99%
“…1, while referring to the previous work of the present author and collaborators, [2][3][4] Yamamoto asserts that "Thus, we think that the dominant factor that made a large difference in their calculations is the choice of the reference point in the virial estimator, rather than whether the estimator was evaluated analytically or numerically via finite difference…." Neither the present author nor his collaborators have suggested that the technique utilized to compute the derivatives might be the cause of the differences in the behavior of the estimators.…”
mentioning
confidence: 99%
“…Neither the present author nor his collaborators have suggested that the technique utilized to compute the derivatives might be the cause of the differences in the behavior of the estimators. Rather, they have pointed out 3,4 that there might be intrinsic differences in the estimators, differences that Yamamoto correctly identifies in Ref. 1.…”
mentioning
confidence: 99%