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Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems
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10.1063/1.3682241
/content/aip/journal/jcp/136/9/10.1063/1.3682241
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/9/10.1063/1.3682241

Figures

Image of FIG. 1.
FIG. 1.

Fluctuation-dissipation theorem for . Solid line represents while triangles are the values of as obtained through Eq. (26).

Image of FIG. 2.
FIG. 2.

The three sets of pictures depict the Γ-dependence of the partition function (P 0), and the ratio of the 1st order correction to the partition function (P 1/P 0) as a function of the system width parameter Γ, at three different temperatures.

Image of FIG. 3.
FIG. 3.

Optimization curve for a low temperature case: , and . The optimized parameter is determined to be Γ = 1.65.

Image of FIG. 4.
FIG. 4.

Normalized diagonal element of the reduced density matrix in the tunneling regime for different values of the cutoff frequency of the Ohmic bath and moderate friction (). The dashed line represents the classical distribution, which is centered on the bottom of the wells and whose height (not shown in the picture) is 1.987. The temperature is = 25. The optimized value of the system width parameter is Γ = 1.65 for and Γ = 2.25 for .

Image of FIG. 5.
FIG. 5.

Normalized diagonal element of the reduced density matrix in the tunneling regime for different values of the cutoff frequency of the Ohmic bath and strong friction (). The temperature is = 25. The optimized value of the system width parameter is Γ = 3.75 for and Γ = 4.5 for .

Tables

Generic image for table
Table I.

Dependence of the crossover temperature on the friction strength in presence of a bath of oscillators.

Generic image for table
Table II.

Optimized Gaussian width for different parameters.

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/content/aip/journal/jcp/136/9/10.1063/1.3682241
2012-03-01
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/9/10.1063/1.3682241
10.1063/1.3682241
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