Correlated noise

[fweik]

The langevin thermostat uses maximally correlated noise for the translation and rotation thermalization.

[RudolfWeeber]

A different RNG salt has to be used for translation and rotation.

Test fragment

    def test_correlations(self):
        """Checks that velocity components are uncorrelated"""

        system=self.system
        system.time_step=0.01
        system.cell_system.skin=0.1
        system.part.add(id=(1,2),pos=np.zeros((2,3)))
        vel_obs = ParticleVelocities(ids=system.part[:].id)
        vel_series = TimeSeries(obs=vel_obs)
        system.auto_update_accumulators.add(vel_series)
        
        if espressomd.has_features("ROTATION"):
            system.part[:].rotation=(1,1,1)
            omega_obs = ParticleBodyAngularVelocities(ids=system.part[:].id)
            omega_series=TimeSeries(obs=omega_obs)
            system.auto_update_accumulators.add(omega_series)
        kT=3.2
        system.thermostat.set_langevin(kT=kT,gamma=2.1,seed=17)
        steps=int(1E5)
        system.integrator.run(steps)

        vel = np.array(vel_series.time_series())
        for i in range(6):
          for j in range(i+1,6):
            print(i,j,np.sum(vel[:,i]*vel[:,j]/steps))
            #self.assertAlmostEqual(np.sum(vel[:,i]*vel[:,j]),0)
        if espressomd.has_features("ROTATION"): 
            omega = np.array(omega_series.time_series())
            for i in range(6):
              for j in range(i+1,6):
                #self.assertClose(np.dot(omega[:,i],omega[:,j]),0)
                print(i,j,np.sum(omega[:,i]*omega[:,j]))
            for i in range(6):
              for j in range(6):
                #self.assertAlmostEqual(np.dot(vel[:,i],omega[:,j]),0)
                print(i,j,np.sum(vel[:,i]*omega[:,j])/steps/kT)