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Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics
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10.1063/1.2786451
/content/aip/journal/jcp/127/17/10.1063/1.2786451
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/17/10.1063/1.2786451

Figures

Image of FIG. 1.
FIG. 1.

The functions in Eq. (17).

Image of FIG. 2.
FIG. 2.

The functions in Eq. (23).

Image of FIG. 3.
FIG. 3.

An example of the “L curve,” taken from an application to the velocity autocorrelation function of liquid parahydrogen at . The regularization parameter decreases by a factor of 0.9 between successive calculations (open circles).

Image of FIG. 4.
FIG. 4.

The curvature of the L curve and the optimum value of the regularization parameter for the example in Fig. 3.

Image of FIG. 5.
FIG. 5.

Canonical real time autocorrelation functions for the anharmonic oscillator in Eq. (35), with . Filled circles: Exact. Dotted lines: RPMD prior. Solid lines: .

Image of FIG. 6.
FIG. 6.

Imaginary time autocorrelation functions for the anharmonic oscillator in Eq. (35), with .

Image of FIG. 7.
FIG. 7.

Canonical real time velocity autocorrelation functions for liquid parahydrogen at 25 and .

Image of FIG. 8.
FIG. 8.

Imaginary time velocity autocorrelation functions for liquid parahydrogen at 25 and . The present imaginary time path integral results (filled circles) agree to graphical accuracy with the results in Fig. 1 of the paper by Rabani et al. (Ref. 21), which were obtained using a different estimator for the imaginary time velocity autocorrelation function (see Appendix A).

Image of FIG. 9.
FIG. 9.

Canonical velocity autocorrelation spectra for liquid parahydrogen at 25 and .

Image of FIG. 10.
FIG. 10.

Thermally symmetrized velocity autocorrelation functions for liquid parahydrogen at . The filled circles are the complex time path integral results of Nakayama and Makri (Ref. 48), and MEAC denotes the MEAC procedure with a flat prior [Eq. (60)].

Image of FIG. 11.
FIG. 11.

Kubo-transformed intermediate scattering functions for liquid orthodeuterium at , for three different momentum transfers .

Image of FIG. 12.
FIG. 12.

Normalized dynamic structure factors for liquid orthodeuterium at , for three different momentum transfers. The calculated structure factors have been normalized such that to facilitate the comparison with experiment. The open circles are the neutron scattering results of Mukherjee et al. (Ref. 56).

Image of FIG. 13.
FIG. 13.

Canonical velocity autocorrelation spectra for liquid parahydrogen at 25 and , obtained using three different priors in the MEAC procedure.

Tables

Generic image for table
Table I.

Results of the L curve procedure using three different priors, for the canonical velocity autocorrelation spectrum of liquid parahydrogen.

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/content/aip/journal/jcp/127/17/10.1063/1.2786451
2007-11-07
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/17/10.1063/1.2786451
10.1063/1.2786451
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