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Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator
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10.1063/1.2742384
/content/aip/journal/jcp/126/20/10.1063/1.2742384
http://aip.metastore.ingenta.com/content/aip/journal/jcp/126/20/10.1063/1.2742384
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Illustrates the effect of negative curvature on determining for the quartic potential . The solid, dashed, and dotted lines represent Eqs. (19), (22), and (24), respectively. The value of that enters the definition of is determined from the global minimum of the QHD-2 potential, making Eq. (24) independent of .

Image of FIG. 2.
FIG. 2.

The average energy for potential (27) is shown for the quantum case (solid line), global minimization (dashed line), local minimization (short dashed line), and the classical potential plus ZPE with global minimization (dotted line). Part (a) gives the shape of the potential and the first few energy levels. Parts (b), (c), and (d) represent defined by Eqs. (19), (22), and (24), respectively. Note that the global case gives the best result overall, especially in (c).

Image of FIG. 3.
FIG. 3.

Average energy for potential (28). See Fig. 2 for details. Again note that the global minimization of in (c) gives the best result.

Image of FIG. 4.
FIG. 4.

Average energy for potential (29). See Fig. 2 for details. Note the failure of all methods in the low temperature limit for (a). This is due to the large negative curvature of the potential. Again, the global minimization gives the best overall result.

Image of FIG. 5.
FIG. 5.

Average energy for potential (30). See Fig. 2 for details. Note the failure of all methods in the low temperature limit for (a). This is due to the large negative curvature of the potential. Again, the global minimization gives the best overall result.

Image of FIG. 6.
FIG. 6.

Thermal phase space weight for potential (29), Fig. 4, plotted vs temperature and position. Part (a) gives the thermal phase space weight using Eq. (22) and global minimization. Part (b) gives the thermal phase space weight using Eq. (19) and global minimization. Part (b) overweights the energetically less accessible portion of the potential, where the curvature becomes negative.

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/content/aip/journal/jcp/126/20/10.1063/1.2742384
2007-05-30
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator
http://aip.metastore.ingenta.com/content/aip/journal/jcp/126/20/10.1063/1.2742384
10.1063/1.2742384
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