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Register a new userComment on Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability, arXiv:0804.0730v1
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We demonstrate that the data presented in the manuscript by Y. Roichman et al. are not sufficient to show that the circulation of a trapped particle exists in a static optical trap.
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We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This non-equilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by non-conservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.
Recently, Huang, Wu and Florin posted a Comment (0806.4632v1) on our preprint (0804.0730v1) describing nonequilibrium circulation of a colloidal sphere trapped in a optical tweezer. The Comment suggests that evidence for toroidal probability currents obtained from experiments and simulations in the original posting should be considered inconclusive. The authors concerns are based on two claims: (1) that Brownian dynamics simulations of the trapped particles motions reveal no statistically significant circulation, and (2) that a realistic description of the radiation pressure acting on the trapped sphere is inconsistent with the motion we have described. In this Reply, we demonstrate both of these claims to be incorrect, and thus the original results and conclusions in 0804.0730v1 to be still valid.
We consider a model of a particle trapped in a harmonic optical trap but with the addition of a non-conservative radiation induced force. This model is known to correctly describe experimentally observed trapped particle statistics for a wide range of physical parameters such as temperature and pressure. We theoretically analyse the effect of non-conservative force on the underlying steady state distribution as well as the power spectrum for the particle position. We compute perturbatively the probability distribution of the resulting non-equilibrium steady states for all dynamical regimes, underdamped through to overdamped and give expressions for the associated currents in phase space (position and velocity). We also give the spectral density of the trapped particles position in all dynamical regimes and for any value of the non-conservative force. Signatures of the presence non-conservative forces are shown to be particularly strong for in the underdamped regime at low frequencies.
G. Brambilla et al. Reply to a Comment by J. Reinhardt et al. questioning the existence of equilibrium dynamics above the critical volume fraction of colloidal hard spheres predicted by mode coupling theory.
We theoretically study the non-monotonic (re-entrant) activated dynamics associated with a repulsive glass to fluid to attractive glass transition in high density particle suspensions interacting via strong short range attractive forces. The classic theoretical projection approximation that replaces all microscopic forces by a single effective force determined solely by equilibrium pair correlations is revisited based on the projectionless dynamic theory (PDT) that avoids force projection. A hybrid-PDT is formulated that explicitly quantifies how attractive forces induce dynamical constraints, while singular hard core interactions are treated based on the projection approach. Both the effects of interference between repulsive and attractive forces, and structural changes due to attraction-induced bond formation that competes with caging, are included. Combined with the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation, the resultant approach appears to properly capture both the re-entrant dynamic crossover behavior and the strong non-monotonic variation of the activated structural relaxation time with attraction strength and range at very high volume fractions. Qualitative differences with ECNLE theory-based results that adopt the full projection approximation are identified, and testable predictions made. The new formulation appears qualitatively consistent with multiple experimental and simulation studies, and provides a new perspective for the overall problem that is rooted in activated motion and interference between repulsive and attractive forces. This is conceptually distinct from empirical shifting or other ad hoc modifications of ideal mode coupling theory which do not take into account activated dynamics. Implications for thermal glass forming liquids are briefly discussed.
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