Changho Kim

Brownian motion from molecular dynamics

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.

Rate description of Fokker-Planck processes with time-periodic parameters

The large time dynamics of a periodically driven Fokker–Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equations of motion are formulated for these three sets of functions and strategies are discussed how to solve them. These methods are illustrated and their usefulness is demonstrated by means of the example of a bistable Brownian oscillator within a large range of driving frequencies from the slow semiadiabatic to the fast driving regime.

Qubit Geometry and Conformal Mapping

AbstractIdentifying the Bloch sphere with the Riemann sphere (the extended complex plane), we obtain relations between single qubit unitary operations and Möbius transformations on the extended complex plane. PACS: 03.67.-a, 03.67.Lx, 03.67.Hk

Quantification of sampling uncertainty for molecular dynamics simulation

We analyze two standard methods to compute the diffusion coefficient of a tracer particle in a medium from molecular dynamics (MD) simulation, the velocity autocorrelation function (VACF) method, and the mean-squared displacement (MSD) method. We show that they are equivalent in the sense that they provide the same mean values with the same level of statistical errors. We obtain analytic expressions for the level of the statistical errors present in the time-dependent diffusion coefficient as well as the VACF and the MSD. Under the assumption that the velocity of the tracer particle is a Gaussian process, all results are expressed in terms of the VACF. Hence, the standard errors of all relevant quantities are computable once the VACF is obtained from MD simulation. By using analytic models described by the Langevin equations driven by Gaussian white noise and Poissonian white shot noise, we verify our theoretical error estimates and discuss the non-Gaussianity effect in the error estimates when the Gaussian process approximation does not hold exactly. For validation, we perform MD simulations for the self-diffusion of a Lennard-Jones fluid and the diffusion of a large and massive colloid particle suspended in the fluid. Our theoretical framework is also applicable to mesoscopic simulations, e.g., Langevin dynamics and dissipative particle dynamics.

Time Correlation Functions of Brownian Motion and Evaluation of Friction Coefficient in the Near-Brownian-Limit Regime

The exponentially decaying behavior of the momentum-momentum and momentum-force time correlation functions of Brownian motion at large times has been extensively used for the numerical evaluation of the friction coefficient

A general scheme for studying the stochastic dynamics of a parametric oscillator driven by coloured noise

\gamma

Numerical method for solving stochastic differential equations with Poissonian white shot noise.

from molecular dynamics simulations. We perform numerical analysis on these methods and address issues related to the appropriate choice of large time and the rate of convergence of these methods. To this end, we obtain asymptotic expansions of the time correlation functions with respect to the reduced mass

Numerical method for solving stochastic differential equations with dichotomous noise

\mu

Thermodynamics of d-dimensional hard sphere fluids confined to micropores

of the Brownian particle. For two important limit procedures of achieving the Brownian limit, certain forms of the asymptotic expansion of the Mori memory function

Wall-mediated self-diffusion in slit and cylindrical pores.

K(t)