Dynamics of a multimode system coupled to multiple heat baths probed by two-dimensional infrared spectroscopy

Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.     

Dynamical correlations in Brownian hard rods

We analyze the time decay of small amplitude density perturbations in systems of highly packed Brownian hard rods, relaxing towards a uniform density distribution. The results of Brownian dynamics simulations and those of the deterministic dynamic density functional (DDF) theory, are contrasted with a new theoretical approach beyond the DDF assumptions. We characterize dynamical correlation modes which, having the lowest relaxation time, determine the late time evolution of the system. The spectrum of possible time decays has a continuous band structure, with pockets of discrete values, near the minima of the DDF results, where the validity of that theory appears to be well established.     

Phase-space approach to dynamical density functional theory

The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.     

The kinetics of overcoming the “entropy barrier”

The escape of a point particle from a cavity of an arbitrary configuration through a small orifice in a cavity wall is considered as a model of entropy barrier overcoming. The dynamics of the particle is determined by collisions with the wall and the dissipative action of the medium. As in reactions with overcoming energy barriers (the Kramers theory), three characteristic regimes can be identified depending on the intensity of friction: diffusion and intermediate regimes and the region of weak friction. For all of them, analytic dependences of rate constants on problem parameters were obtained. The procedure for sewing solutions together, similar to that employed in the Kramers theory, gives a unified equation for the transmission factor over the whole range of friction values. In the weak friction mode, overcoming the entropy barrier generally leads to a nonexponential kinetics.     

Comparison between theoretical values and simulation results of viscosity for the dissipative particle dynamics method

In order to investigate the validity of the dissipative particle dynamics method, which is a mesoscopic simulation technique, we have derived an expression for viscosity from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expressions of the viscosity due to momentum and dissipative forces have been obtained using the approximate solutions of the distribution functions. Also, we have conducted nonequilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method. The theoretical values of the viscosity due to dissipative forces in the Hoogerbrugge-Koelman theory are in good agreement with the simulation results obtained by the nonequilibrium dynamics method, except in the range of small number densities. There are restriction conditions for taking appropriate values of the number density, number of particles, time interval, shear rate, etc., to obtain physically reasonable results by means of dissipative particle dynamics simulations.     

Collisional line shapes for low frequency vibrations of adsorbates on a metal surface

The dynamics of atoms or molecules adsorbed on a metal surface, and excited by collisions with an atomic beam, are treated within a theory that includes energy dissipation into lattice vibrations by means of a frequency and temperature dependent friction function. The theory provides dynamic structure factors for energy transfer derived from collisional time correlation functions. It describes the relaxation of a vibrationally excited atom or molecule within a model of a damped quantum harmonic oscillator bilinearly coupled to a bath of lattice oscillators. The collisional time correlation function is generalized to include friction effects and is applied to the vibrational relaxation of the frustrated translation mode of Na adsorbed on a Cu(001) surface, CO on Cu(001), and CO on Pt(111), following excitation by collisions with He atoms. Results for the frequency shift and width of line shapes versus surface temperature are in very good agreement with experimental measurements of inelastic He atom scattering. Our interpretation of the experimental results provides insight on the relative role of phonon versus electron-hole relaxation.     

Improved configuration space sampling: Langevin dynamics with alternative mobility

We present a new and efficient method for determining optimal configurations of a large number (N) of interacting particles. We use a coarse-grained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton's method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface Phi. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of Phi. We employ a Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.     

Transport of a heated granular gas in a washboard potential

We study numerically the motion of a one dimensional array of Brownian particles in a washboard potential, driven by an external stochastic force and interacting via short range repulsive forces. In particular, we investigate the role of instantaneous elastic and inelastic collisions on the system dynamics and transport. The system displays a locked regime, where particles may move only via activated processes and a running regime where particles drift along the direction of the applied field. By tuning the value of the friction parameter controlling the Brownian motion we explore both the overdamped dynamics and the underdamped dynamics. In the two regimes we considered the mobility and the diffusivity of the system as functions of the tilt and other relevant control parameters such as coefficient of restitution, particle size, and total number of particles. We find that while in the overdamped regime the results for the interacting systems present similarities with the known noninteracting case, in the underdamped regime the inelastic collisions determine a rich variety of behaviors among which is an unexpected enhancement of the inelastic diffusion.     

Electrokinetics of diffuse soft interfaces. 2. Analysis based on the nonlinear Poisson-Boltzmann equation

In a previous study (Langmuir 2004, 20, 10324), the electrokinetic properties of diffuse soft layers were theoretically investigated within the framework of the Debye-Hückel approximation valid in the limit of sufficiently low values for the Donnan potential. In the current paper, the electrokinetics is tackled on the basis of the rigorous nonlinearized Poisson-Boltzmann equation, the numerical evaluation of the electroosmotic velocity profile, and the analytically derived hydrodynamic velocity profile. The results are illustrated and discussed for a diffuse soft interface characterized by a linear gradient for the friction coefficient and the density of hydrodynamically immobile ionogenic groups in the transition region separating the bulk soft layer and the bulk electrolyte solution. In particular, it is shown how the strong asymmetry for the potential distribution, as met for high values of the bulk fixed charge density and/or low electrolyte concentrations, is reflected in the electrokinetic features of the diffuse soft layer. The analysis clearly highlights the shortcomings of the discontinuous approximation by Ohshima and others for the modeling of the friction and electrostatic properties of soft layers exhibiting high Donnan potentials. This is in line with reported electrokinetic measurements of various soft particles and permeable gels at low electrolyte concentrations which fail to match predictions based on Ohshima's theory.     

Second-order quantized Hamilton dynamics coupled to classical heat bath

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.     

Inelastic hard rods in a periodic potential

A simple model of inelastic hard rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat bath. We explore the effect of the spatial nonuniformity on the steady states of the system. The spatial variations of the density, granular temperature, and pressure induced by the gradient of the external potential are investigated and compared with the analogous variations in an elastic system. Finally, we study the clustering process by considering the relaxation of the system starting from a uniform homogeneous state.     

Escape from a cavity through a small window: turnover of the rate as a function of friction constant

To escape from a cavity through a small window the particle has to overcome a high entropy barrier to find the exit. As a consequence, its survival probability in the cavity decays as a single exponential and is characterized by the only parameter, the rate constant. We use simulations to study escape of Langevin particles from a cubic cavity through a small round window in the center of one of the cavity walls with the goal of analyzing the friction dependence of the escape rate. We find that the rate constant shows the turnover behavior as a function of the friction constant, zeta: The rate constant grows at very small zeta, reaches a maximum value which is given by the transition-state theory (TST), and then decreases approaching zero as zeta-->infinity. Based on the results found in simulations and some general arguments we suggest a formula for the rate constant that predicts a turnover of the escape rate for ergodic cavities in which collisions of the particle with the cavity walls are defocusing. At intermediate-to-high friction the formula describes transition between two known results for the rate constant: the TST estimation and the high friction limiting behavior that characterizes escape of diffusing particles. In this range of friction the rate constants predicted by the formula are in good agreement with those found in simulations. At very low friction the rate constants found in simulations are noticeably smaller than those predicted by the formula. This happens because the simulations were run in the cubic cavity which is not ergodic.     

Microcomputer-aided optimal selection of control input for the precision water bath of a heat exchange calorimeter

In heat exchange calorimetry, sample and reference vessels are fixed differentially in a water bath. The heat evolved in the sample vessel is exchanged freely with the ambient water. The accuracy and precision of the calorimetry depend on the temperature range of the drift and fluctuation in the bath water. In the present report, a simple temperature-control system with no empirical factors is proposed for the precision water bath. The heat exchange between the inside of the vessels and the ambient water is expressed by a differential equation or a Newtonian cooling equation. Similarly, the thermal behaviour of a water bath placed in a non-air-conditioned laboratory was also considered to be expressed by the same equation. The heat exchanged with the surroundings, the non-stationary heat flow from warm stirrer motors, and other thermal factors were considered to be part of the heat sources. Cooling water about 2°C lower than the set temperature was circulated in the water bath. The difference between the set temperature and the observed temperature was fed into a microcomputer every second. The latest four data points were used to fit a modified Newtonian equation by the common method of least-squares. The control input to the bath was calculated and given to the heater circuit after power amplification. The program written in basic was about 3.3 kbyte. The controlled range of drift and fluctuation was almost the same, or better, as that previously reported.     

Time-dependent density functional theory of open quantum systems in the linear-response regime

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Go?rling-Levy perturbation theory is calculated.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.