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Langevin thermostat

In Langevin dynamics [63], the temperature is maintained by modifying the Newton's equations of motion:

$\displaystyle \dot{r_i} = p_i/m_i \qquad \dot{p_i} = F_i - {\gamma}_i p_i + f_i,\ $ (6.33)

where $ F_i$ is the force acting on atom $ i$ due to the interaction potential, $ {\gamma}_i$ is a friction coefficient, and $ f_i$ is a random force with dispersion $ \sigma_i$ related to the friction coefficient $ \gamma_i$ via:

$\displaystyle \sigma_i^2 = 2\,m_i\,{\gamma}_i\,k_B\,T/{\Delta}t$ (6.34)

with $ {\Delta}t$ being the time-step used in MD to integrate equations of motion. Obviously, Langevin dynamics is identical to classical Hamiltonian in the limit of vanishing $ \gamma$.

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