The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.
We report, from direct observation of particle trajectories as a function of time, the presence of stringlike cooperative motion in a quasi-two-dimensional liquid. We have used digital video microscopy to study the equilibrium dynamics of suspensions of sterically stabilized uncharged poly(methylmethacrylate) spheres confined in a thin glass cell. Our experiments reveal the existence, in semidilute and dense liquid states, of a transition in the qualitative dynamical behavior of the system. At short times particles undergo unhindered Brownian motion, at intermediate times they undergo uncorrelated binary collisions, and at long times these one-particle self-diffusive modes are coupled to collective longitudinal acoustic modes of the fluid, the signature of which is local fluctuating domains of enhanced particle mobility. We study the properties of these domains by examining the density dependence of the van Hove self-correlation function and its deviation from Gaussian behavior. We observe that periods of non-Gaussian behavior correlate precisely with the timing of events involved in the relaxation of "caged" particles and their nearest neighbors. In contrast with relaxation processes in supercooled liquids, the lifetime of dynamical heterogeneities in a dissipative colloidal suspension is found to shift towards shorter time scales with increasing particle density. During time periods for which a quasi-two-dimensional system follows Gaussian behavior, we observe that, as predicted by Cichocki and Felderhof [J. Phys. Condens. Matter 6, 7287 (1994)], the time dependence of the evolution of the effective diffusion coefficient from its short time to its long time value has the form (ln t)/t. This last finding is true for all observed particle densities. To our knowledge, these results are the first experimental verification of the existence of microscopic cooperativity and the predicted temporal evolution of the diffusion coefficient for Brownian motion in concentrated quasi-two-dimensional liquids.
In this paper the ab initio potential of mean force for the formic acid-water system is calculated in a Monte Carlo simulation using a classical fluctuating charge molecular mechanics potential to guide Monte Carlo updates. The ab initio energies in the simulation are calculated using density-functional theory ͑DFT͒ methods recently developed by Salahub et al. ͓J. Chem. Phys. 107, 6770 ͑1997͔͒ to describe hydrogen-bonded systems. Importance sampling methods are used to investigate structural changes and it is demonstrated that using a molecular mechanics importance function can improve the efficiency of a DFT simulation by several orders of magnitude. Monte Carlo simulation of the system in a canonical ensemble at Tϭ300 K reveals two chemical processes at intermediate time scales: The rotation of the H 2 O bonded to HCOOH, which takes place on a time scale of 3 ps, and the dissociation of the complex which occurs in 24 ps. It is shown that these are the only important structural ''reactions'' in the formic acid-water cluster which take place on a time scale shorter than the double transfer of the proton.
Collective motion in nonequilibrium steady state suspensions of self-propelled Janus motors driven by chemical reactions can arise due to interactions coming from direct intermolecular forces, hydrodynamic flow effects, or chemotactic effects mediated by chemical gradients. The relative importance of these interactions depends on the reactive characteristics of the motors, the way in which the system is maintained in a steady state, and properties of the suspension, such as the volume fraction. From simulations of a microscopic hard collision model for the interaction of fluid particles with the Janus motor we show that dynamic cluster states exist and determine the interaction mechanisms that are responsible for their formation. The relative importance of chemotactic and hydrodynamic effects is identified by considering a microscopic model in which chemotactic effects are turned off while the full hydrodynamic interactions are retained. The system is maintained in a steady state by means of a bulk reaction in which product particles are reconverted into fuel particles. The influence of the bulk reaction rate on the collective dynamics is also studied.
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