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On the origin and convergence of a post-quantization constrained propagator for path integral simulations of rigid bodies
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10.1063/1.4803118
/content/aip/journal/jcp/138/18/10.1063/1.4803118
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4803118
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Upper panel: Difference between PQC and exact (E) particle on a ring density -basis diagonal matrix element as a function of τ (in units of inverse Kelvin). The plot is focusing on very small values of τ. Values of from 0 to 8 are shown. Lower panel: Same quantity as in the upper panel with a logarithmic scale for both axis. The dashed line corresponds to a model power law of exponent .

Image of FIG. 2.
FIG. 2.

Difference between PQC and exact (E) particle on a ring energy estimator (in energy units of Kelvin) obtained directly from the -basis diagonal matrix element as a function of τ (in units of inverse Kelvin). The plot is focusing on very small values of τ. Values of from 0 to 8 are shown.

Image of FIG. 3.
FIG. 3.

Upper panel: Difference between PQC and exact (E) linear rigid rotor density (ℓ, )-basis diagonal matrix element as a function of τ (in units of inverse Kelvin). The plot is focusing on very small values of τ. Values of ℓ from 0 to 8 are shown. Lower panel: Same quantity as in the upper panel with a logarithmic scale for both axis. The dashed line corresponds to a model power law of exponent 2.

Image of FIG. 4.
FIG. 4.

Difference between PQC and exact (E) linear rigid rotor energy estimator (in energy units of Kelvin) obtained directly from the (ℓ, )-basis diagonal matrix element as a function of τ (in units of inverse Kelvin). The plot is focusing on very small values of τ. Values of ℓ from 0 to 8 are shown.

Image of FIG. 5.
FIG. 5.

Path integral energies (in units of K) obtained with a SOS thermal propagator for a planar rotor with a periodic potential as a function of the imaginary time step (in units of reciprocal energy K) and their quadratic fit, at a temperature T = 0.37 K. The blue star corresponds to the exact FBR average energy at the same temperature.

Image of FIG. 6.
FIG. 6.

Path integral energies (in units of K) obtained with a PQC thermal propagator for a planar rotor with a periodic potential as a function of the imaginary time step (in units of reciprocal energy K) and their linear fit, at a temperature T = 0.37 K. The blue star corresponds to the exact FBR average energy at the same temperature.

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/content/aip/journal/jcp/138/18/10.1063/1.4803118
2013-05-08
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the origin and convergence of a post-quantization constrained propagator for path integral simulations of rigid bodies
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4803118
10.1063/1.4803118
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