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A variational principle in Wigner phase-space with applications to statistical mechanics
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10.1063/1.3519637
/content/aip/journal/jcp/134/3/10.1063/1.3519637
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/3/10.1063/1.3519637

Figures

Image of FIG. 1.
FIG. 1.

The imaginary time development of the variational parameters α(τ), γ(τ) of the quartic oscillator DF.

Image of FIG. 2.
FIG. 2.

Plot of quartic oscillator ground-state Wigner functions.

Image of FIG. 3.
FIG. 3.

Thermalized flux distribution at β = 12 obtained using the variational principle with one basis function compared to an accurate calculation.

Image of FIG. 4.
FIG. 4.

Thermalized flux distribution at β = 12 obtained using the variational principle with two basis functions compared to an accurate calculation. Initial value of n(2) = −0.001.

Image of FIG. 5.
FIG. 5.

Flux-side CF’s from CW model based on accurate and variational thermal flux DF’s. Also shown is the accurate quantum CF.

Image of FIG. 6.
FIG. 6.

Values of the “population” parameters n(1), n(2) and n(3) for the tunneling dynamics in the double-well.

Image of FIG. 7.
FIG. 7.

Time variation of the average position 〈q〉 of the Wigner DF for models (i), (ii), and a classical model. Also shown is the accurate time-dependent average position of the Wigner DF.

Image of FIG. 8.
FIG. 8.

Time variation of the average position 〈q〉 of the Wigner DF for model (ii) with and without constraint. Also shown is the accurate time-dependent average position of the Wigner DF.

Tables

Generic image for table
Table I.

Transmission coefficients (κ) for the Eckart barrier at β = 12 obtained from the CW method using different thermal flux DF’s as input. Also shown is the accurate quantum mechanical value (QM) taken from Ref. 10. acc, var and bf means accurate, variational and basis function, respectively.

Generic image for table
Table II.

Thermal average value for quartic oscillator at various temperatures.

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/content/aip/journal/jcp/134/3/10.1063/1.3519637
2011-01-21
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A variational principle in Wigner phase-space with applications to statistical mechanics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/3/10.1063/1.3519637
10.1063/1.3519637
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