Stress Tensor Autocorrelation Function¶

This module calculates the autocorrelation of the off-diagonal elements of the stess tensor $\Pi_{\alpha\beta}$ :

$C_{\alpha\beta}(t) = \frac{1}{N} \langle \Pi_{\alpha\beta}(t) \Pi_{\alpha\beta}(0) \rangle \, \text{.}$

By normalisation with the particle number $N$ , the result remains finite in the thermodynamic limit. The stress tensor is obtained from halmd.observables.thermodynamics.stress_tensor().

The shear viscosity $\eta$ is found from this autocorrelation via the Green–Kubo relation

$\eta = \frac{\rho}{k_B T} \int_0^\infty \! C_{\alpha\beta}(t) \, \mathrm{d}t \, \text{.}$

Note

The module returns the sum over all off-diagonal elements, $\sum_{\alpha < \beta} C_{\alpha\beta}(t)$ , analogously to halmd.observables.dynamics.mean_square_displacement.

class halmd.observables.dynamics.stress_tensor_autocorrelation(args)¶

Construct stress tensor autocorrelation function.

This module implements a halmd.observables.dynamics.correlation module.

Parameters:	args – keyword arguments args.thermodynamics – instance of `halmd.observables.thermodynamics`

acquire()¶

Acquire stress tensor

Returns:	Stress tensor sample

correlate(first, second)¶

Correlate two stress tensor samples.

Parameters:	first – first phase space sample second – second phase space sample
Returns:	stress tensor autocorrelation function between two samples.

desc¶: Module description.

class writer(args)¶

Construct file writer.

Parameters:	args (table) – keyword arguments args.file – instance of file writer args.location (string table) – location within file (optional)
Returns:	file writer as returned by `file:writer()`.

The argument location specifies a path in a structured file format like H5MD given as a table of strings. It defaults to {"dynamics", self.label, "stress_tensor_autocorrelation"}.

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Stress Tensor Autocorrelation Function¶

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