Langevin Dynamics [ld]

This section sets the option for the Langevin Dynamics.

Integrators

Currently two different integrators are implemented, which are specified with the type option:

type: string

the integrator to use

The available options are “bussi-parinello” and “overdamped”.

The Bussi-Parinello option uses the algorithm and the thermostat described by Bussi and Parinello [4].

The respective Langevin equation is

\[\mathop{}\!\mathrm{d} p(t) = - \nabla U(q) \mathop{}\!\mathrm{d} t - \gamma p(t) \mathop{}\!\mathrm{d} t + \sqrt{2 m \gamma \beta^{-1} } \mathop{}\!\mathrm{d} W (t)\]

The update rule for the overdamped integrator is a Euler-Maruyama scheme [5] given by the simpler equation that was e.g. used in [6]:

\[x(t+\Delta t) = x(t) - \Delta t \nabla U(x(t)) + \sqrt{2 \Delta t} W (t+\Delta t)\]

Options

timestep: float

integration time step in dimensionless units

n_steps: int

number of time steps the simulation should run

seed: int, optional

starting seed for the random number generator of the noise term

kt: float, required only for bussi-parinello

thermal energy of the simulation in energy units (\(k_B T = \beta^{-1}\))

friction: float, required only for bussi-parinello

friction parameter \(\gamma\)

Example

[ld]
type: bussi-parinello
timestep: 0.005
kt: 1.0
friction: 10.0
n_steps: 10000

References