sarkas.tools.observables.PressureTensor.sum_rule

PressureTensor.sum_rule(beta, rdf, potential)

Calculate the sum rule integrals from the rdf.

\begin{eqnarray} \sigma_{zzzz} & = & \frac{n}{\beta^2} \left [ 3 + \frac{2\beta}{15} I^{(1)} + \frac{\beta}{5} I^{(2)} \right ] , \\ \sigma_{zzxx} & =& \frac{n}{\beta^2} \left [ 1 - \frac{2\beta}{5} I^{(1)} + \frac {\beta}{15} I^{(2)} \right ] , \\ \sigma_{xyxy} & = & \frac{n}{\beta^2} \left [ 1 + \frac{4\beta}{15} I^{(2)} + \frac {\beta}{15} I^{(2)} \right ] , \end{eqnarray}

where \(I^{(k)} = \sum_{A} \sum_{B \geq A}I_{AB}^{(\rm {Hartree}, k)} + I_{AB}^{(\rm {Corr}, k)}\) calculated from sarkas.tools.observables.RadialDistributionFunction.compute_sum_rule_integrals().

Parameters

• beta (float) – Inverse temperature factor. Grab it from sarkas.tools.observables.Thermodynamics.beta.

• rdf (sarkas.tools.observables.RadialDistributionFunction) – Radial Distribution function object.

• potential (sarkas.potentials.core.Potential) – Potential object.

Returns

• sigma_zzzz (float) – See above integral.

• sigma_zzxx (float) – See above integral.

• sigma_xyxy (float) – See above integral.