# Re: Are random forces applied at every step (when using the langevin thermostat) ?

From: Jérôme Hénin (jerome.henin_at_ibpc.fr)
Date: Mon Apr 29 2013 - 03:58:22 CDT

Hi Ajasja,

Interesting question.

> Are random forces applied at each step or at a fixed time interval
> (for example every 1 ps) when using the langevin thermostat?

Random forces are applied at every timestep. The "damping" parameter can be understood as a decay time for inertia: beyond that time scale, the particles lose memory of their velocities due to the Langevin bath.

> The reason for this question is as follows:
> If I run a simulation with 0.1, 1 or 10 fs time-step, then the random
> forces would be applied 10000 1000 or 100 times during one ps of
> simulation. This might mean that the dynamics of the system
> (strongly?) depends on the time-step, which intuitively should not
> be the case.

More precisely, very short-time properties of the dynamics depend on the time step. If you divide the time step by ten, you'll apply random forces ten times more frequently, but they will have one tenth the variance. The statistical properties of the result are the same, because at the end of the day, the integrated stochastic forces are a sum of independent random variables. Of course, the smaller the damping, the less noticeable this will be even at short times.

This is almost the same thing as impulse-based multiple time-stepping, where one applies long-range forces in pulses at essentially arbitrary (small) intervals, and the resulting long time dynamics is correct. The only difference here is that the forces are stochastic, so the magnitude of the impulse doesn't depend linearly on the time interval, but its square (the variance) does.

For numerical sanity, the only criterion that comes to my mind is that the time step should be much smaller than the correlation time, otherwise you get overdamped Langevin dynamics, not MD in the traditional sense.

Cheers,
Jerome

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