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:
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.

connect(args)
Parameters:

  • args (table) – keyword arguments

  • args.every – sampling interval

Returns:

sequence of signal connections

Internal use only. This function is called upon registration by blocking_scheme:correlation().

Connect msv.group.particle:aux_enable() to the signal on_prepend_force of halmd.observables.sampler using the interval every.

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"}.