# ngce.m

From Spinach Documentation Wiki

Numerical integral route to the Redfield relaxation superoperator.

## Contents

## Syntax

R=ngce(spin_system,H,dt)

## Arguments

H0 - static laboratory frame Hamiltonian commutation su- peroperator acting in the background H1 - stochastic part of the laboratory frame Hamiltonian commutation superoperator with a zero average, as a K by N cell array with the following topology: {H(0) H(dt) H(2dt) ... H(Ndt); % MD trajectory 1 H(0) H(dt) H(2dt) ... H(Ndt); % MD trajectory 2 ............................ H(0) H(dt) H(2dt) ... H(Ndt)}; % MD trajectory K i.e. the rows are made of individual MD trajectories. dt - time step of the MD trajectory, seconds

## Outputs

R - laboratory frame relaxation superoperator

## Examples

A test against the analytical relaxation superoperator is provided in examples/relaxation_theory/ngce_test.m file.

## Notes

Enough trajectory points must be present to converge each integral, and enough trajectories must be present to converge the average.

## See also

relaxation.m, lindbladian.m, magpump.m

*Version 2.5, authors: Ilya Kuprov, Jim Prestegard*