Stochastic processes: Time evolution, symmetries and linear response

Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology

The present theoretical understanding of various properties of superionic conductors is reviewed. Emphasis is put on their treatment as classical many-particle systems and on the analysis of their dynamic behaviour. Different kinds of approaches pertaining to the low frequency dynamics are considered in detail. They include stochastic models, like hopping or Fokker-Planck models as well as a hydrodynamic theory. The high frequency (phonon-) dynamics and the information obtained from computer simulations is also analysed. As far as possible, the relevance of the different approaches with respect to experiments on specific materials is discussed. Possible directions for future investigations are outlined.

Theoretical models for superionic conductors

Solitons in condensed matter: A paradigm

The structure of aqueous suspensions of electrostatically interacting submicron polymer spheres is studied as a function of shear. These model colloidal suspensions exhibit a variety of equilibrium and nonequilibrium structures and phase transitions. Both shear induced melting of solid-like structures and shear induced distortion of liquid-like structures are observed. Several models are presented to explain the observed effects. The analogy between these colloidal suspensions and pure fluid systems is discussed.

Sheared colloidal suspensions

We study the steady-state dynamical behavior of a set of torsion-coupled pendula in the presence of damping, fluctuating thermal torques, and constant applied torque For small applied torque, the average angular velocity of the pendula at low temperature is associated with the motion of thermalized sine-Gordon solitons, and, as the torque is increased, the velocity response becomes strongly nonlinear These results can be used to describe nonlinear response in Josephson transmission lines and weakly pinned one-dimensional charge-density-wave condensates

Brownian motion of coupled nonlinear oscillators: Thermalized solitons and nonlinear response to external forces

The Euler-Lagrange equation for an impurity interacting with an inhomogeneous fluid is derived and applied to a description of the polarized hydrogen system, ${\mathrm{H}}_{\mathrm{\ensuremath{\uparrow}}}$, ${\mathrm{D}}_{\mathrm{\ensuremath{\uparrow}}}$, and ${\mathrm{T}}_{\mathrm{\ensuremath{\uparrow}}}$ on the surface of liquid $^{4}\mathrm{He}$. We find well-defined, strongly bound physisorbed states for ${\mathrm{T}}_{\mathrm{\ensuremath{\uparrow}}}$, and ${\mathrm{D}}_{\mathrm{\ensuremath{\uparrow}}}$ and a weakly bound physisorbed state for ${\mathrm{H}}_{\mathrm{\ensuremath{\uparrow}}}$.

Interaction of atomic hydrogen with the surface of liquid /sup 4/He

The finite-temperature commensurability problem is formulated and reduced to the solution of a transfer-integral problem. Numerical solutions for the free energy, equation of state, one- and two-particle densities,..., provide a detailed description of the behavior of epitaxial systems at $T\ensuremath{\ne}0$.

M. D. Miller

Papers

Brownian motion of coupled nonlinear oscillators: Thermalized solitons and nonlinear response to external forces

Interaction of atomic hydrogen with the surface of liquid /sup 4/He

Commensurability in One Dimension at T≠0