54,801 research outputs found
Complex Langevin Dynamics for chiral Random Matrix Theory
We apply complex Langevin dynamics to chiral random matrix theory at nonzero
chemical potential. At large quark mass the simulations agree with the
analytical results while incorrect convergence is found for small quark masses.
The region of quark masses for which the complex Langevin dynamics converges
incorrectly is identified as the region where the fermion determinant
frequently traces out a path surrounding the origin of the complex plane during
the Langevin flow. This links the incorrect convergence to an ambiguity in the
Langevin force due to the presence of the logarithm of the fermion determinant
in the action.Comment: 23 pages, 10 figure
Memory effects in non-adiabatic molecular dynamics at metal surfaces
We study the effect of temporal correlation in a Langevin equation describing
non-adiabatic dynamics at metal surfaces. For a harmonic oscillator the
Langevin equation preserves the quantum dynamics exactly and it is demonstrated
that memory effects are needed in order to conserve the ground state energy of
the oscillator. We then compare the result of Langevin dynamics in a harmonic
potential with a perturbative master equation approach and show that the
Langevin equation gives a better description in the non-perturbative range of
high temperatures and large friction. Unlike the master equation, this approach
is readily extended to anharmonic potentials. Using density functional theory
we calculate representative Langevin trajectories for associative desorption of
N from Ru(0001) and find that memory effects lowers the dissipation of
energy. Finally, we propose an ab-initio scheme to calculate the temporal
correlation function and dynamical friction within density functional theory
Dynamics of Langevin Simulation
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical
simulations of quantum field theories based on stochastic quantization and the
Langevin equation. The topics discussed include renormalization of finite
step-size algorithms, Fourier acceleration, and the relation of the Langevin
equation to hybrid stochastic algorithms and hybrid Monte Carlo.Comment: 20 p
Brownian Motors driven by Particle Exchange
We extend the Langevin dynamics so that particles can be exchanged with a
particle reservoir. We show that grand canonical ensembles are realized at
equilibrium and derive the relations of thermodynamics for processes between
equilibrium states. As an application of the proposed evolution rule, we devise
a simple model of Brownian motors driven by particle exchange. KEYWORDS:
Langevin Dynamics, Thermodynamics, Open SystemsComment: 5 pages, late
New Langevin and Gradient Thermostats for Rigid Body Dynamics
We introduce two new thermostats, one of Langevin type and one of gradient
(Brownian) type, for rigid body dynamics. We formulate rotation using the
quaternion representation of angular coordinates; both thermostats preserve the
unit length of quaternions. The Langevin thermostat also ensures that the
conjugate angular momenta stay within the tangent space of the quaternion
coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have
constructed three geometric numerical integrators for the Langevin thermostat
and one for the gradient thermostat. The numerical integrators reflect key
properties of the thermostats themselves. Namely, they all preserve the unit
length of quaternions, automatically, without the need of a projection onto the
unit sphere. The Langevin integrators also ensure that the angular momenta
remain within the tangent space of the quaternion coordinates. The Langevin
integrators are quasi-symplectic and of weak order two. The numerical method
for the gradient thermostat is of weak order one. Its construction exploits
ideas of Lie-group type integrators for differential equations on manifolds. We
numerically compare the discretization errors of the Langevin integrators, as
well as the efficiency of the gradient integrator compared to the Langevin ones
when used in the simulation of rigid TIP4P water model with smoothly truncated
electrostatic interactions. We observe that the gradient integrator is
computationally less efficient than the Langevin integrators. We also compare
the relative accuracy of the Langevin integrators in evaluating various static
quantities and give recommendations as to the choice of an appropriate
integrator.Comment: 16 pages, 4 figure
Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems
When simulating molecular systems using deterministic equations of motion
(e.g., Newtonian dynamics), such equations are generally numerically integrated
according to a well-developed set of algorithms that share commonly agreed-upon
desirable properties. However, for stochastic equations of motion (e.g.,
Langevin dynamics), there is still broad disagreement over which integration
algorithms are most appropriate. While multiple desiderata have been proposed
throughout the literature, consensus on which criteria are important is absent,
and no published integration scheme satisfies all desiderata simultaneously.
Additional nontrivial complications stem from simulating systems driven out of
equilibrium using existing stochastic integration schemes in conjunction with
recently-developed nonequilibrium fluctuation theorems. Here, we examine a
family of discrete time integration schemes for Langevin dynamics, assessing
how each member satisfies a variety of desiderata that have been enumerated in
prior efforts to construct suitable Langevin integrators. We show that the
incorporation of a novel time step rescaling in the deterministic updates of
position and velocity can correct a number of dynamical defects in these
integrators. Finally, we identify a particular splitting that has essentially
universally appropriate properties for the simulation of Langevin dynamics for
molecular systems in equilibrium, nonequilibrium, and path sampling contexts.Comment: 15 pages, 2 figures, and 2 table
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