Langevin thermostat

The Langevin thermostat maintains the temperature through a modification of Newton's equations of motion

${\dot {r_{i}}}=p_{i}/m_{i}\qquad {\dot {p_{i}}}=F_{i}-{\gamma }_{i}\,p_{i}+f_{i},$

where F_i is the force acting on atom i due to the interaction potential, γ_i is a friction coefficient, and f_i is a random force simulating the random kicks by the damping of particles between each other due to friction. The random numbers are chosen from a Gaussian distribution with the following variance

$\sigma _{i}^{2}=2\,m_{i}\,{\gamma }_{i}\,k_{B}\,T/{\Delta }t$

with Δt being the time-step used in the MD to integrate the equations of motion. Obviously, Langevin dynamics is identical to the classical Hamiltonian in the limit of vanishing γ.

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