Transport Phenomena at Rough Boundaries

We present a simple method describing transport processes near rough boundaries. By a proper coordinate transformation we reduce a transport problem with rough walls to an equivalent problem with smooth flat walls, but with some random bulk inhomogeneities. In many cases the last problem can be treated perturbatively, leading to simple expressions for relevant transport coefficients via the correlation function of surface inhomogeneities. We calculate diffusion and conductivity in films, phonon, and photon diffusion, quantum corrections to conductivity, and the single-particle diffusion coefficient

Boundary Effects and Spin Waves in Spin-Polarized Quantum Gases

Boundary conditions are derived for spin dynamics of spin-polarized quantum gases near nonmagnetic walls. We are interested mostly in boundary-induced line shifts and attenuation of spin waves, and in the possibility of having a macroscopic boundary condition for systems close to a Knudsen ballistic regime. We consider the effects caused by roughness of the wall and by surface adsorption. By a proper coordinate transformation, we reduce the problem of particle collisions with an inhomogeneous nonmagnetic wall to an equivalent problem with a specular homogeneous wall but with stochastic bulk imperfections. As a result, the boundary effects are described by some additional bulklike transverse spin-diffusion coefficient inversely proportional to the angular harmonics of the correlation function of surface inhomogeneities. This leads to an effective macroscopiclike boundary condition for transverse spin dynamics responsible for the boundary effects in spin-wave resonances. The situation changes drastically at low temperatures because of an appearance of an adsorbed boundary layer which renormalizes the molecular field near the wall, and leads to additional effective spin-exchange processes. The experimental implications for helium and hydrogen systems are discussed

Transport in Channels and Films with Rough Surfaces

We present a simple and versatile description of transport of almost ballistic particles near rough boundaries with an emphasis on thin films and narrow channels. The main effects are associated with chaotization of motion as a result of repeated scattering from random walls. We show that the problem contains an additional mesoscopic length scale which is expressed explicitly via the amplitude and correlation radius (or the correlation function) of surface inhomogeneities, and the ratio of the particle wavelength to the correlation radius. The calculations are performed with the help of a canonical coordinate transformation which reduces a transport problem with rough random walls to a completely equivalent problem with ideal flat walls, but with some random bulk distortions. This problem is treated on the basis of a kinetic equation with a perturbative collision integral. In addition to the application of the Boltzmann transport equation for (quasi)particles with an arbitrary degree of degeneracy of the distribution function, we also include the results for a single-particle diffusion on the basis of the Focker-Plank equation. We calculate different transport coefficients for (quasi)particles with an arbitrary spectrum ε(p) with a bulk of calculations for particles with quadratic, p2/2m, and linear, cp, spectra. The calculations are made in classic and WKB regimes as well as in the case of quantized motion across the film. All the transport coefficients are expressed via the first two angular harmonics of the correlation function of surface inhomogeneities which play the role of an effective transport cross section. The results include the effects of bulk impurities and changes in potential relief near the walls. We also calculate the quantum interference corrections to conductivity and localization and mesoscopic effects associated with reflections from random surface inhomogeneities, and the density of states in low-dimensional films. The mesoscopic properties are especially simple in the case of strong quantization of motion across the d-dimensional films when the problem becomes effectively equivalent to localization of d-1-dimensional motion in weak random potential. We discuss possible future applications of our method such as for porous media, boundary slip, etc

Statistical Quasiparticles in Transverse Dynamics of Gases

We analyze the validity of the Fermi-liquid approach to transverse dynamics of spin-polarized gases at arbitrary temperatures. We demonstrate that the diagrammatic kinetic equation for transverse processes can be formulated as a simpler, but completely equivalent equation in terms of ‘‘statistical quasiparticles.’’ The equation includes all coherent and dephasing molecular-field terms as well as the dissipative collision integral up to the second order. Beyond the second order, the results become very complicated, and a quasiparticle approach loses its attraction. We give the expressions for the effective interaction function and collision integral for statistical quasiparticles, applicable at all temperatures, and discuss the implications of this concept at high temperatures. The interaction function contains anomalous pole terms which do not exist in equations for longitudinal dynamics. This provides a somewhat unexpected interpretation for zero-temperature dissipative processes, observed recently in spin dynamics, and for controversial molecular field terms (the so-called I2 terms) as imaginary (pole) and real (principal) parts of the quasiparticle interaction function. These molecular field terms with complicated analytical structure do not vanish completely, as was assumed earlier, in the Boltzmann region, but contribute to higher-order density terms. With an emphasis on quantum gases, we discuss how to reconcile various physical assumptions inherent to different kinetic approaches to dilute gases

Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach