arXiv subjects

Thorsten Emig

Publications and source records attributed to Thorsten Emig.

At least 37 records · Page 2Linked to original sources

arXiv2015

Casimir--Polder force between anisotropic nanoparticles and gently curved surfaces

The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

quant-ph↗

arXiv2015

Critical Casimir Force between Inhomogeneous Boundaries

To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.

cond-mat.stat-mech↗

arXiv2014

Interplay of curvature and temperature in the Casimir-Polder interaction

We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.

quant-ph↗

arXiv2014

Effect of Curvature and Confinement on the Casimir-Polder Interaction

Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in- and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.

cond-mat.stat-mech↗

arXiv2014

Casimir-Polder interaction for gently curved surfaces

We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits.

quant-ph↗

arXiv2014

Heat transfer between anisotropic nanopartricles: Enhancement and switching

We theoretically study heat transfer between two anisotropic nanoparticles in vacuum, and derive closed expressions in terms of the anisotropic dipole polarizabilities. We show that transfer between two small spheroids can be many times as large as the one for two spheres of same volumes. Such increase with anisotropy is also found for the heat emission of an isolated small spheroid. Furthermore, we observe a strong dependence of transfer on the relative orientation, yielding the interpretation as a heat transfer switch. The switch quality, given as the ratio of transfer in the ``on'' and ``off'' positions, is observed to be as large as $10^3$ in the near field and even larger in the far field.

quant-ph↗

arXiv2012

Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.

quant-ph↗

arXiv2012

Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals

We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity $σ$. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length $λ_{\rm p}$ while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation.

cond-mat.stat-mech↗

arXiv2011

Dilution and resonance enhanced repulsion in non-equilibrium fluctuation forces

In equilibrium, forces induced by fluctuations of the electromagnetic field between electrically polarizable objects (microscopic or macroscopic) in vacuum are always attractive. The force may, however, become repulsive for microscopic particles coupled to thermal baths with different temperatures. We demonstrate that this non-equilibrium repulsion can be realized also between macroscopic objects, as planar slabs, if they are kept at different temperatures. It is shown that repulsion can be enhanced by (i) tuning of material resonances in the thermal region, and by (ii) reducing the dielectric contrast due to "dilution". This can lead to stable equilibrium positions. We discuss the realization of these effects for aerogels, yielding repulsion down to sub-micron distances at realistic porosities.

quant-ph↗

arXiv2011

Universality versus material dependence of fluctuation forces between metallic wires

We calculate the Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity $σ$ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of $σ$. At smaller separations, we compute the interaction numerically and observe an approach to the proximity approximation.

cond-mat.stat-mech↗

arXiv2011

Non-equilibrium electromagnetic fluctuations: Heat transfer and interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in non-equilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.

quant-ph↗

arXiv2011

Non-equilibrium Casimir forces: Spheres and sphere-plate

We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.

quant-ph↗

arXiv2011

Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.

quant-ph↗

arXiv2010

Casimir potential of a compact object enclosed by a spherical cavity

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.

quant-ph↗

arXiv2010

Casimir force between sharp-shaped conductors

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

quant-ph↗

arXiv2010

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.

quant-ph↗

arXiv2010

Casimir Force at a Knife's Edge

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $θ$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.

quant-ph↗

arXiv2010

Casimir Physics: Geometry, Shape and Material

The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these interactions. It is based on a combination of methods from statistical physics and scattering theory. We showcase how it is exquisitely suited to analyze a variety of previously unexplored phenomena. Examples are given to show how the interplay of geometry and material properties helps to understand and control these forces.

cond-mat.stat-mech↗