Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem

We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models which consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol'd tongues in the regime of low ac-driving amplitude or high ac-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro's argument that holds in the perturbative regime of large driving amplitudes or low driving frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte

Dynamic ordering and frustration of confined vortex rows studied by mode-locking experiments

The flow properties of confined vortex matter driven through disordered mesoscopic channels are investigated by mode locking (ML) experiments. The observed ML effects allow to trace the evolution of both the structure and the number of confined rows and their match to the channel width as function of magnetic field. From a detailed analysis of the ML behavior for the case of 3-rows we obtain ({\it i}) the pinning frequency $f_p$, ({\it ii}) the onset frequency $f_c$ for ML ($\propto$ ordering velocity) and ({\it iii}) the fraction $L_{ML}/L$ of coherently moving 3-row regions in the channel. The field dependence of these quantities shows that, at matching, where $L_{ML}$ is maximum, the pinning strength is small and the ordering velocity is low, while at mismatch, where $L_{ML}$ is small, both the pinning force and the ordering velocity are enhanced. Further, we find that $f_c \propto f_p^2$, consistent with the dynamic ordering theory of Koshelev and Vinokur. The microscopic nature of the flow and the ordering phenomena will also be discussed.Comment: 10 pages, 7 figure, submitted to PRB. Discussion has been improved and a figure has been adde

Geometry and material effects in Casimir physics - Scattering theory

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.Comment: 44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics volume in Casimir physic

Microscopic theory of retarded Van der Waals forces between macroscopic dielectric bodies

In a previous paper we derived an expression for the retarded Van der Waals interaction energy at zero temperature in an arbitrary system of atoms, where an atom was represented by an isotropic harmonic oscillator with one resonance frequency. Starting from this expression we evaluate in this paper the interaction energy between an atom and a semi-infinite dielectric medium, consisting of the same kind of atoms, and that between two dielectric halfspaces. The expressions for the interaction energy can be given in terms of the dielectric constant of the medium, and in this way formulae, earlier derived by Lifshitz from macroscopic considerations are recovered. Limiting formulae for both systems are obtained in the case of small and large separation of the two bodies; furthermore, the first correction (3-particle contribution) to the additive result (2-particle contribution) is given in these limiting cases for both systems

Microscopic theory of retarded Van der Waals forces between macroscopic dielectric bodies

In a previous paper we derived an expression for the retarded Van der Waals interaction energy at zero temperature in an arbitrary system of atoms, where an atom was represented by an isotropic harmonic oscillator with one resonance frequency. Starting from this expression we evaluate in this paper the interaction energy between an atom and a semi-infinite dielectric medium, consisting of the same kind of atoms, and that between two dielectric halfspaces. The expressions for the interaction energy can be given in terms of the dielectric constant of the medium, and in this way formulae, earlier derived by Lifshitz from macroscopic considerations are recovered. Limiting formulae for both systems are obtained in the case of small and large separation of the two bodies; furthermore, the first correction (3-particle contribution) to the additive result (2-particle contribution) is given in these limiting cases for both systems

Microscopic derivation of macroscopic Van der Waals forces

For a general system of isotropic harmonic oscillators with non-retarded dipole interaction a formula for the interatomic forces is derived. It is used to give an atomistic derivation of macroscopic Van der Waals forces in terms of the dielectric constant