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A new post-quantization constrained propagator for rigid tops for use in path integral quantum simulations
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10.1063/1.4829506
/content/aip/journal/jcp/139/18/10.1063/1.4829506
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/18/10.1063/1.4829506
View: Figures

## Figures

FIG. 1.

Difference between PQC and Exact (E) spherical top density operator (thermal propagator) (, , )-basis diagonal matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 3 are shown. The dashed line corresponds to a model power law of exponent 5/2.

FIG. 2.

Difference between PQC and Exact (E) spherical top energy estimator (, , )-basis diagonal matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 3 are shown. The linear convergence towards the Exact SOS estimator, up to a constant shift (not included in the PQC energy), is explicitly apparent.

FIG. 3.

Difference between PQC and Exact (E) symmetric top density operator (thermal propagator) (, , )-basis diagonal (, ||)-matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 3 are shown. The dashed line corresponds to a model power law of exponent 5/2.

FIG. 4.

Difference between PQC and Exact (E) symmetric top energy estimator (, , )-basis (, ||)-diagonal matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 3 are shown. The linear convergence towards the Exact SOS estimator, up to a constant shift, is explicitly apparent.

FIG. 5.

Difference between PQC and Exact (E) asymmetric top density operator (thermal propagator) (, , )-basis -matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 2 are shown. The dashed line corresponds to a model power law of exponent 5/2.

FIG. 6.

Difference between PQC and Exact (E) asymmetric top energy estimator (, , )-basis -matrix element as a function of τ (in units of inverse Kelvin) in logarithmic scale for both axis. The plot is focusing on very small values of τ. Values of from 0 to 2 are shown. The linear convergence towards the Exact SOS estimator, up to a constant shift, is explicitly apparent.

FIG. 7.

Path integral Monte Carlo energies (in units of K) obtained with a PQC thermal propagator for an asymmetric top as a function of the imaginary time step (in units of reciprocal energy K−1) and their linear fit, at a temperature = 10 K. The blue star corresponds to the exact FBR average energy at the same temperature.

/content/aip/journal/jcp/139/18/10.1063/1.4829506
2013-11-14
2014-04-17

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