Langevin thermostat: Difference between revisions
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The Langevin thermostat maintains the temperature through a modification of Newton's equations of motion | The Langevin thermostat{{cite|allen:book:1991}}{{cite|hoover:prl:1982}}{{cite|evans:jcp:1983}} maintains the temperature through a modification of Newton's equations of motion | ||
:<math> | :<math> | ||
\dot{r_i} = p_i/m_i \qquad | \dot{r_i} = p_i/m_i \qquad | ||
Revision as of 11:54, 31 May 2019
The Langevin thermostat[1][2][3] maintains the temperature through a modification of Newton's equations of motion
- [math]\displaystyle{ \dot{r_i} = p_i/m_i \qquad \dot{p_i} = F_i - {\gamma}_i\,p_i + f_i, }[/math]
where Fi is the force acting on atom i due to the interaction potential, γi is a friction coefficient, and fi is a random force with dispersion σi related to γi through:
- [math]\displaystyle{ \sigma_i^2 = 2\,m_i\,{\gamma}_i\,k_B\,T/{\Delta}t }[/math]
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.
References