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Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation
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10.1063/1.2981065
/content/aip/journal/jcp/129/12/10.1063/1.2981065
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/12/10.1063/1.2981065

Figures

Image of FIG. 1.
FIG. 1.

Imaginary time autocorrelation function for the harmonic oscillator with the mass and at the inverse temperature . Solid line: exact results. Hollow cycles: the MEAC using the flat prior with the “L-curve” technique (MEAC-flat-L). Solid triangles: the MEAC using the flat prior with the CME technique (MEAC-flat-CME).

Image of FIG. 2.
FIG. 2.

Comparison of the LSC-IVR to the MEAC-flat for the standard real time autocorrelation functions for the harmonic oscillator with the mass and at the inverse temperature . Panel (b) shows a blowup of the curves shown in (a).

Image of FIG. 3.
FIG. 3.

Comparison of the LSC-IVR to the MEAC-flat at a relatively high temperature for the quartic potential with the mass and : (a) Standard momentum autocorrelation function (divided by 2 m) and (b) Kubo-transformed force autocorrelation function, the force .

Image of FIG. 4.
FIG. 4.

Comparison of imaginary time data transformed from the corresponding real time autocorrelation functions based on the LSC-IVR to those based on the for the quartic potential at the inverse temperatures : (a) The imaginary momentum autocorrelation function (divided by 2 m) and (b) the imaginary force autocorrelation function . Solid line: exact results. Hollow cycles: the MEAC using the LSC-IVR prior with the “L-curve” technique (MEAC-LSC/IVR-L). Solid triangles: the MEAC using the LSC-IVR prior with the CME technique (MEAC-LSC/IVR-CME). Long-dashed line: the LSC-IVR.

Image of FIG. 5.
FIG. 5.

Comparison of the standard momentum autocorrelation function (divided by 2 m) [panel (a)] and the Kubo-transformed force autocorrelation function [panel (b)] from the LSC-IVR to those from the for the quartic potential at the inverse temperature .

Image of FIG. 6.
FIG. 6.

Same as in Fig. 4, but at the inverse temperature .

Image of FIG. 7.
FIG. 7.

Same as in Fig. 5, but at the inverse temperature .

Image of FIG. 8.
FIG. 8.

The imaginary momentum autocorrelation function per particle (divided by ) transformed from the corresponding Kubo-transformed real time correlation function from different trajectory-based approaches (LSC-IVR, RPMD, CMD, and classical dynamics) for liquid para- at two state points: (a) and (b) .

Image of FIG. 9.
FIG. 9.

Spectra of Kubo-transformed momentum autocorrelation functions for the liquid para- at the state point . Comparison among different trajectory-based approaches [panel (a)], comparison among the MEAC results with different priors [panel (b)], and comparisons of each prior to its MEAC correction [panels (c)–(f)].

Image of FIG. 10.
FIG. 10.

Same as in Fig. 9, but at the different state points: . 

Image of FIG. 11.
FIG. 11.

Kubo-transformed momentum autocorrelation functions (divided by ) for the liquid para- at the state point: . Comparison among different trajectory-based approaches [panel (a)], comparison among the MEAC results with different priors [panel (b)], and comparisons between the LSC-IVR (and its MEAC-corrected version) to each of other trajectory-based approaches (and their MEAC corrections) [panels (c)–(e)].

Image of FIG. 12.
FIG. 12.

Same as in Fig. 11, but at the different state points: .

Image of FIG. 13.
FIG. 13.

The function defined in Eq. (A7) as a function of , which demonstrates how the imaginary time data affect the real time data in the interval and vice versa.

Tables

Generic image for table
Table I.

Information entropies in the MEAC procedure for different priors for liquid para-hydrogen at and under nearly zero extent pressure.

Generic image for table
Table II.

Diffusion constants for liquid para-hydrogen at under nearly zero extent pressure.

Generic image for table
Table III.

Diffusion constants for liquid para-hydrogen at under nearly zero extent pressure.

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/content/aip/journal/jcp/129/12/10.1063/1.2981065
2008-09-29
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/12/10.1063/1.2981065
10.1063/1.2981065
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