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Inclusion of inversion symmetry in centroid molecular dynamics: A possible avenue to recover quantum coherence
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10.1063/1.2358989
/content/aip/journal/jcp/125/16/10.1063/1.2358989
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/16/10.1063/1.2358989

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Centroid densities at and for the quartic potential of Eq. (27) are shown for . The solid line represents , dotted line , and dashed line .

Image of FIG. 2.
FIG. 2.

(Color online) Centroid position autocorrelation functions obtained from the SA-CMD (dotted line) at and for the quartic potential of Eq. (27). The exact result (solid line) is shown for comparison. The superscripts denote the symmetrization and antisymmetrization operations.

Image of FIG. 3.
FIG. 3.

(Color online) Power spectra of the position autocorrelation functions at and are for the quartic potential of Eq. (27). Exact (solid line), CMD (dotted line), and combined SA-CMD (dashed line) results are shown.

Image of FIG. 4.
FIG. 4.

(Color online) Real parts of the position autocorrelation functions at and for the quartic potential of Eq. (27). Exact (solid line), CMD (dotted line), and combined SA-CMD (dashed line) results are shown. For each value, two different time ranges are plotted.

Image of FIG. 5.
FIG. 5.

(Color online) Centroid densities at and for the double-well potential of Eq. (28) are shown for . The solid line represents , dotted line , and dashed line .

Image of FIG. 6.
FIG. 6.

(Color online) Centroid position autocorrelation functions obtained from the SA-CMD (dotted line) at and for the double-well potential of Eq. (28). The exact result (solid line) is shown for comparison. The superscripts denote the symmetrization and antisymmetrization operations.

Image of FIG. 7.
FIG. 7.

(Color online) Power spectra of the position autocorrelation functions at and for the double-well potential of Eq. (28). Exact (solid line), CMD (dotted line), and combined SA-CMD (dashed line) results are shown. Peaks at from approximate methods are due to the fact that their time correlation functions neither converge to nor oscillate about zero.

Image of FIG. 8.
FIG. 8.

(Color online) Real parts of the position autocorrelation functions at and for the double-well potential of Eq. (28). Exact (solid line), CMD (dotted line), and combined SA-CMD (dashed line) results are shown. For each value, two different time ranges are plotted.

Image of FIG. 9.
FIG. 9.

(Color online) Trajectory plots are shown over centroid phase space from to for the double-well potential of Eq. (28) with . Exact (fine solid line), CMD (thick solid line), and combined SA-CMD (fine dashed line) results are shown. The two different initial conditions, and , are represented by diamond symbols.

Tables

Generic image for table
Table I.

Partition functions for quartic potential Eq. (27) and double-well potential Eq. (28) are presented.

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/content/aip/journal/jcp/125/16/10.1063/1.2358989
2006-10-25
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Inclusion of inversion symmetry in centroid molecular dynamics: A possible avenue to recover quantum coherence
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/16/10.1063/1.2358989
10.1063/1.2358989
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