About Langevin Dynamics.

From: Boyang Wang (pkuwangboyang_at_yahoo.com.cn)
Date: Wed Mar 01 2006 - 12:18:30 CST

Hi Jerome and all,
   
  I found your previous email. That is really helpful. But my question is:
   
   
  The Gamma in Langevin equation should have a unit of (s)^-1, as "mass*gamma*v" has the unit of force.
   
  But in NAMD configuration files, the Langevin damping coefficient has a unit of (s) or (ps), which puzzles me. I thought this Langevin damping coefficient was the reciprocal of the "gamma" in the Langevin equation.
   
  Thanks for all your time.
   
  Boyang.
   
   
   
  Tue Mar 02 2004 - 15:39:24 CST
   
  Jrôme wrote:
   
  "
  When doing Langevin dynamics, NAMD adds two forces to those deriving from the
force field :
* a frictional force, equal to - mass * gamma * velocity (gamma is the damping
coefficient)
* a stochastic force, that is normally distributed with zero average and a rms
value sigma.
  As I said previously, the frictional term constantly drains the system's
kinetic energy, while the stochastic force gives back a certain amount of
energy.
To use this as a thermostat, the force rms, sigma, has to be adjusted using
the fluctuation-dissipation theorem. In this case, the FDT yields :
sigma = sqrt( 2 * kT * gamma * mass / delta_t), where delta_t is the timestep.
  So NAMD uses the value of gamma provided by the user and computes accordingly
the value of sigma that will lead to the desired temperature. You can see
that if gamma is very small, sigma will be small too, so that the overall
Langevin force will be negligible compared to "physical" ones from the force
field.
  All this is likely to be explained with much detail in nonequilibrium
statistical mechanics books.
  Cheers,
Jerome
"

                
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