658 research outputs found
Elastic Constants of Quantum Solids by Path Integral Simulations
Two methods are proposed to evaluate the second-order elastic constants of
quantum mechanically treated solids. One method is based on path-integral
simulations in the (NVT) ensemble using an estimator for elastic constants. The
other method is based on simulations in the (NpT) ensemble exploiting the
relationship between strain fluctuations and elastic constants. The strengths
and weaknesses of the methods are discussed thoroughly. We show how one can
reduce statistical and systematic errors associated with so-called primitive
estimators. The methods are then applied to solid argon at atmospheric
pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good
agreement with available experimental data on elastic constants is found for
helium 3. Predictions are made for the thermal expectation value of the kinetic
energy of solid helium 3.Comment: 9 pages doublecolumn, 6 figures, submitted to PR
Colored-noise thermostats \`a la carte
Recently, we have shown how a colored-noise Langevin equation can be used in
the context of molecular dynamics as a tool to obtain dynamical trajectories
whose properties are tailored to display desired sampling features. In the
present paper, after having reviewed some analytical results for the stochastic
differential equations forming the basis of our approach, we describe in detail
the implementation of the generalized Langevin equation thermostat and the
fitting procedure used to obtain optimal parameters. We discuss in detail the
simulation of nuclear quantum effects, and demonstrate that, by carefully
choosing parameters, one can successfully model strongly anharmonic solids such
as neon. For the reader's convenience, a library of thermostat parameters and
some demonstrative code can be downloaded from an on-line repository
The Coupled Electronic-Ionic Monte Carlo Simulation Method
Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion
Monte Carlo or Path Integral Monte Carlo are the most accurate and general
methods for computing total electronic energies. We will review methods we have
developed to perform QMC for the electrons coupled to a classical Monte Carlo
simulation of the ions. In this method, one estimates the Born-Oppenheimer
energy E(Z) where Z represents the ionic degrees of freedom. That estimate of
the energy is used in a Metropolis simulation of the ionic degrees of freedom.
Important aspects of this method are how to deal with the noise, which QMC
method and which trial function to use, how to deal with generalized boundary
conditions on the wave function so as to reduce the finite size effects. We
discuss some advantages of the CEIMC method concerning how the quantum effects
of the ionic degrees of freedom can be included and how the boundary conditions
can be integrated over. Using these methods, we have performed simulations of
liquid H2 and metallic H on a parallel computer.Comment: 27 pages, 10 figure
Efficient molecular dynamics using geodesic integration and solvent-solute splitting
We present an approach to Langevin dynamics in the presence of holonomic constraints based on decomposition of the system into components representing geodesic flow, constrained impulse and constrained diffusion. We show that a particular ordering of the components results in an integrator that is an order of magnitude more accurate for configurational averages than existing alternatives. Moreover, by combining the geodesic integration method with a solventâsolute force splitting, we demonstrate that stepsizes of at least 8âfs can be used for solvated biomolecules with high sampling accuracy and without substantially altering diffusion rates, approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems. The methods described in this article are easily implemented using the standard apparatus of modern simulation codes
Molecular Dynamics Simulations
A tutorial introduction to the technique of Molecular Dynamics (MD) is given,
and some characteristic examples of applications are described. The purpose and
scope of these simulations and the relation to other simulation methods is
discussed, and the basic MD algorithms are described. The sampling of intensive
variables (temperature T, pressure p) in runs carried out in the microcanonical
(NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as
well as the realization of other ensembles (e.g. the NVT ensemble). For a
typical application example, molten SiO2, the estimation of various transport
coefficients (self-diffusion constants, viscosity, thermal conductivity) is
discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study
of a glass-forming polymer melt under shear is mentioned.Comment: 38 pages, 11 figures, to appear in J. Phys.: Condens. Matte
Collisionless kinetic theory of rolling molecules
We derive a collisionless kinetic theory for an ensemble of molecules
undergoing nonholonomic rolling dynamics. We demonstrate that the existence of
nonholonomic constraints leads to problems in generalizing the standard methods
of statistical physics. In particular, we show that even though the energy of
the system is conserved, and the system is closed in the thermodynamic sense,
some fundamental features of statistical physics such as invariant measure do
not hold for such nonholonomic systems. Nevertheless, we are able to construct
a consistent kinetic theory using Hamilton's variational principle in
Lagrangian variables, by regarding the kinetic solution as being concentrated
on the constraint distribution. A cold fluid closure for the kinetic system is
also presented, along with a particular class of exact solutions of the kinetic
equations.Comment: Revised version; 31 pages, 1 figur
Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
Steady states and traveling waves play a fundamental role in understanding
hydrodynamic problems. Even when unstable, these states provide the
bifurcation-theoretic explanation for the origin of the observed states. In
turbulent wall-bounded shear flows, these states have been hypothesized to be
saddle points organizing the trajectories within a chaotic attractor. These
states must be computed with Newton's method or one of its generalizations,
since time-integration cannot converge to unstable equilibria. The bottleneck
is the solution of linear systems involving the Jacobian of the Navier-Stokes
or Boussinesq equations. Originally such computations were carried out by
constructing and directly inverting the Jacobian, but this is unfeasible for
the matrices arising from three-dimensional hydrodynamic configurations in
large domains. A popular method is to seek states that are invariant under
numerical time integration. Surprisingly, equilibria may also be found by
seeking flows that are invariant under a single very large Backwards-Euler
Forwards-Euler timestep. We show that this method, called Stokes
preconditioning, is 10 to 50 times faster at computing steady states in plane
Couette flow and traveling waves in pipe flow. Moreover, it can be carried out
using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes
to these popular spectral codes. We explain the convergence rate as a function
of the integration period and Reynolds number by computing the full spectra of
the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid
Dynamics, ed. Alexander Gelfgat (Springer, 2018
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
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