arXiv subjects

Thorsten Emig

Publications and source records attributed to Thorsten Emig.

At least 55 records · Page 3Linked to original sources

arXiv2010

Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models

We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations.

cond-mat.stat-mech↗

arXiv2009

Constraints on stable equilibria with fluctuation-induced forces

We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir/van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also 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.

quant-ph↗

arXiv2009

Casimir interactions of an object inside a spherical metal shell

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.

quant-ph↗

arXiv2009

Scattering Theory Approach to Electrodynamic Casimir Forces

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, nonzero temperatures, and 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. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

quant-ph↗

arXiv2009

Pinning of Flux Lines by Planar Defects

The influence of randomly distributed point impurities and planar defects on order and transport in type-II superconductors and related systems is studied. It is shown that the Bragg glass phase is unstable with respect to planar efects. Even a single weak defect plane oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is a relevant perturbation in the Bragg glass. A defect that is aligned with the magnetic field restores the flux density oscillations which decay algebraically with the distance from the defect. The theory exhibits striking similarities to the physics of a Luttinger liquid with a frozen impurity. The exponent for the flux line creep in the direction perpendicular to a relevant defect is derived. We find that the flux line lattice exhibits in the presence of many randomly distributed parallel planar defects aligned to the magnetic field a new glassy phase which we call planar glass. The planar glass is characterized by diverging shear and tilt moduli, a transverse Meissner effect, resistance against shear deformations. We also obtain sample to sample fluctuations of the longitudinal magnetic susceptibility and an exponential decay of translational long range order in the direction perpendicular to the defects. The flux creep perpendicular to the defects leads to a nonlinear resistivity $ρ(J \to 0)\sim \exp[-(J_D/J)^{3/2}]$. Strong planar defects enforce arrays of dislocations that are located at the defects with a Burgers vector parallel to the defects in order to relax shear strain.

cond-mat.dis-nn↗

arXiv2009

Casimir Forces and Geometry in Nanosystems

This article reviews recent progress on the geometry dependence of Casimir interactions and presents some applications to nanosystems. The article consists of three parts: (i) Some examples for geometry dependence: structured surfaces, cylinders, and spheres. (ii) Material dependence: Casimir interaction between nano-spheres. (iii) Casimir force induced non-linear dynamics, ratchet effects.

cond-mat.stat-mech↗

arXiv2008

Casimir forces between cylinders and plates

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.

cond-mat.stat-mech↗

arXiv2007

Fluctuation induced quantum interactions between compact objects and a plane mirror

The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.

cond-mat.stat-mech↗

arXiv2007

Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

We analyze the Casimir force between two parallel infinite metal cylinders, with nearby metal plates (sidewalls), using complementary methods for mutual confirmation. The attractive force between cylinders is shown to have a nonmonotonic dependence on the separation to the plates. This intrinsically multi-body phenomenon, which occurs with either one or two sidewalls (generalizing an earlier result for squares between two sidewalls), does not follow from any simple two-body force description. We can, however, explain the nonmonotonicity by considering the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders, and their images on the nearby plate(s). Furthermore, we show that this effect also implies a nonmonotonic dependence of the cylinder-plate force on the cylinder-cylinder separation.

cond-mat.stat-mech↗

arXiv2007

Casimir force driven ratchets

We explore the non-linear dynamics of two parallel periodically patterned metal surfaces that are coupled by the zero-point fluctuations of the electromagnetic field between them. The resulting Casimir force generates for asymmetric patterns with a time-periodically driven surface-to-surface distance a ratchet effect, allowing for directed lateral motion of the surfaces in sizeable parameter ranges. It is crucial to take into account inertia effects and hence chaotic dynamics which are described by Langevin dynamics. Multiple velocity reversals occur as a function of driving, mean surface distance, and effective damping. These transport properties are shown to be stable against weak ambient noise.

cond-mat.stat-mech↗

arXiv2006

Relation between directed polymers in random media and random bond dimer models

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.

cond-mat.stat-mech↗

arXiv2006

Planar defects and the fate of the Bragg glass phase of type-II superconductors

It is shown that the Bragg glass phase can become unstable with respect to planar defects. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current voltage relation is changed to ln V(J) -J^{-1}. The theory exhibits some similarities to the physics of Luttinger liquids with impurities.

cond-mat.dis-nn↗

arXiv2005

Photon density of states for deformed surfaces

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced.

cond-mat.stat-mech↗

arXiv2005

Ordering of geometrically frustrated classical and quantum Ising magnets

A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model from the quantum dynamics induced by a transverse field. By mapping the Ising models on a triangular lattice to elastic lattices of non-crossing strings, we derive an exact relation between the spin variables and the displacement field of the strings. Using this map both for the classical (2+1)D stacked model and the quantum frustrated 2D system, we obtain a microscopic derivation of an effective Hamiltonian which was proposed before on phenomenological grounds within a Landau-Ginzburg-Wilson approach. In contrast to the latter approach, our derivation provides the coupling constants and hence the entire transverse field--versus--temperature phase diagram can be deduced, including the universality classes of both the quantum and the finite--temperature transitions. The structure of the ordered phase is obtained from a detailed entropy argument. We compare our predictions to recent simulations of the quantum system and find good agreement. We also analyze the connections to a dimer model on the hexagonal lattice and its height profile representation, providing a simple derivation of the continuum free energy and a physical explanation for the universality of the stiffness of the height profile for anisotropic couplings.

cond-mat.stat-mech↗

arXiv2004

Geometry and Spectrum of Casimir Forces

We present a new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and general boundary conditions. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain non-perturbative results for the Casimir interaction between rigid surfaces. As an example, we compute the lateral electrodynamic force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations, complementing known short distance expansions which we also reproduce with high precision.

cond-mat.stat-mech↗

arXiv2004

String Picture of a Frustrated Quantum Magnet and Dimer Model

We map a geometrically frustrated Ising system with transversal field generated quantum dynamics to a strongly anisotropic lattice of non-crossing elastic strings. The combined effect of frustration, quantum and thermal spin fluctuations is explained in terms of a competition between intrinsic lattice pinning of strings and topological defects in the lattice. From this picture we obtain analytic results for correlations and the phase diagram which agree nicely with recent simulations.

cond-mat.stat-mech↗

arXiv2004

Dynamics of granular avalanches caused by local perturbations

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. Following previous studies, we use mass and momentum conservation to derive St-Venant like equations for the evolution of the thickness R of the mobile layer and the profile Z of the static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.

cond-mat.stat-mech↗

arXiv2004

Non perturbative approach to Casimir interactions in periodic geometries

Due to their collective nature Casimir forces can strongly depend on the geometrical shape of the interacting objects. We study the effect of strong periodic shape deformations of two ideal metal plates on their quantum interaction. A non-perturbative approach which is based on a path integral quantization of the electromagnetic field is presented in detail. Using this approach, we compute the force for the specific case of a flat plate and a plate with a rectangular corrugation. We obtain complementary analytical and numerical results which allow us to identify two different scaling regimes for the force as a function of the mean plate distance, corrugation amplitude and wave length. Qualitative distinctions between transversal electric and magnetic modes are revealed. Our results demonstrate the importance of a careful consideration of the non-additivity of Casimir forces, especially in strongly non-planar geometries. Non-perturbative effects due to surface edges are found. Strong deviations from the commonly used proximity force approximation emerge over a wide range of corrugation wave lengths, even though the surface is composed only of flat segments. We compare our results to that of a perturbative approach and a classical optics approximation.

cond-mat.stat-mech↗