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Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics
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10.1063/1.3589406
/content/aip/journal/jcp/134/19/10.1063/1.3589406
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/19/10.1063/1.3589406
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The autocorrelation functions for the one-dimensional harmonic oscillator for β = 8. Panel (a) Kubo-transformed momentum autocorrelation function; (b) Real part of standard x 2 autocorrelation function. Solid line: Exact quantum result; dotted line: LSC-IVR; solid circles: ELD; solid triangles: ECD; solid squares: EHD. Panel (c) Kubo-transformed momentum autocorrelation function. Solid line: Exact quantum result; solid circles: RPMD; solid triangles: CMD with classical operator; solid squares: CMD with effective classical operator. (d) Kubo-transformed x 2 autocorrelation function. Solid line: Exact quantum result; dashed line: RPMD; dotted line: CMD with classical operator; dot-dashed line: CMD with effective classical operator.

Image of FIG. 2.
FIG. 2.

The autocorrelation functions for the one-dimensional anharmonic oscillator for β = 0.1. Solid line: Exact quantum result. In the following results, the Boltzmann operator is treated by TGA. Dotted line: LSC-IVR with full TGA. Solid circles: W-ELD with LGA-TGA. Solid triangles: W-ECD with LGA-TGA. Solid squares: W-EHD with LGA-TGA. Panel (a) Kubo-transformed momentum autocorrelation function; (b) symmetrized force autocorrelation function; (c) real part of standard x 2 autocorrelation function.

Image of FIG. 3.
FIG. 3.

As in Fig. 1, but for a much lower temperature β = 8.

Image of FIG. 4.
FIG. 4.

The autocorrelation functions for the one-dimensional quartic oscillator for β = 0.1. Solid line: Exact quantum result. In the following results, the Boltzmann operator is treated by the TGA. Dotted line: LSC-IVR with full TGA. Solid circles: W-ELD with LGA-TGA. Solid triangles: W-ECD with LGA-TGA. Solid squares: W-EHD with LGA-TGA. Panel (a) Kubo-transformed momentum autocorrelation function; (b) symmetrized force autocorrelation function; (c) real part of standard x 2 autocorrelation function.

Image of FIG. 5.
FIG. 5.

As in Fig. 3, but for a much lower temperature β = 8.

Image of FIG. 6.
FIG. 6.

The autocorrelation functions for the one-dimensional double well potential for β = 0.1 and for β = 8. Panels (a), (c), and (e): Kubo-transformed momentum autocorrelation function. Panels (b), (d), and (f): Real part of standard x 2 autocorrelation function. Panels (a)–(d)—Solid line: Exact quantum result; dotted line: LSC-IVR with LGA-TGA; solid circles: W-ELD with LGA-TGA; solid triangles: W-ECD with LGA-TGA; solid squares: W-EHD with LGA-TGA. Panels (e)–(f)—Solid line: Exact quantum result; Dotted line: LSC-IVR with LGA-TGA; Solid circles: W-ELD with full-TGA; Solid triangles: W-ECD with full-TGA.

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/content/aip/journal/jcp/134/19/10.1063/1.3589406
2011-05-19
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/19/10.1063/1.3589406
10.1063/1.3589406
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