Simen Å. Ellingsen

Repulsive Casimir and Casimir–Polder forces

Casimir and Casimir?Polder repulsions have been known for more than 50 years. The general ?Lifshitz? configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso?s group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on some recent developments will be surveyed. Here, stress will be placed on analytic developments, especially on Casimir?Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker?s 75th birthday devoted to ?Applications of zeta functions and other spectral functions in mathematics and physics?.

Thermal corrections to the Casimir effect

The Casimir effect, reflecting quantum vacuum fluctuations in the electromagnetic field in a region with material boundaries, has been studied both theoretically and experimentally since 1948. The forces between dielectric and metallic surfaces both plane and curved have been measured at the 10–1% level in a variety of room temperature experiments, and remarkable agreement with the zero-temperature theory has been achieved. In fitting the data various corrections due to surface roughness, patch potentials, curvature, and temperature have been incorporated. It is the latter that is the subject of the present paper. We point out that, in fact, no temperature dependence has yet been detected, and that the experimental situation is still too fluid to permit conclusions about thermal corrections to the Casimir effect. Theoretically, there are subtle issues concerning thermodynamics and electrodynamics which have resulted in disparate predictions concerning the nature of these corrections. However, a general consensus has seemed to emerge that suggests that the temperature correction to the Casimir effect is relatively large, and should be observable in future experiments involving surfaces separated at the few micrometre scale.

Thermal Casimir-Polder shifts in Rydberg atoms near metallic surfaces

The Casimir-Polder (CP) potential and transition rates of a Rydberg atom above a plane metal surface at finite temperature are discussed. As an example, the CP potential and transition rates of a rubidium atom above a copper surface at 300 K are computed. Close to the surface we show that the quadrupole correction to the force is significant and increases with increasing principal quantum number n. For both the CP potential and decay rates one finds that the dominant contribution comes from the longest wavelength transition and the potential is independent of temperature. We provide explicit scaling laws for potential and decay rates as functions of atom-surface distance and principal quantum number of the initial Rydberg state.

Transverse radiation force in a tailored optical fiber

We show, by means of simple model calculations, how a weak laser beam sent though an optical fiber exerts a transverse radiation force if there is an azimuthal asymmetry present in the fiber such that one side has a slightly different refractive index than the other. The refractive index difference {Delta}n needs only to be very low, of order 10{sup -3}, to produce an appreciable transverse displacement of order 10 {mu}m. We argue that the effect has probably already been seen in a recent experiment by W. She et al. [Phys. Rev. Lett. 101, 243601 (2008)], and we discuss the correspondence between these observations and the theory presented. The effect could be used to bend optical fibers in a predictable and controlled manner and we propose that it could be useful for micron-scale devices.

How linear surface waves are affected by a current with constant vorticity

The interaction of surface waves with Couette-type current with uniform vorticity is a well suited problem for students approaching the theory of surface waves. The problem, although mathematically simple, contains rich physics, and is moreover important in several situations from oceanography and marine technology to microfluidics. We here lay out a simple two-dimensional theory of waves propagating upon a basic flow of uniform vorticity of constant depth. The dispersion relation is found, showing how the shearing current introduces different phase velocities for upstream and downstream propagating waves. The role of the surface tension is discussed and applied to the case of a wave pattern created by a moving source, stationary as seen by the source. We conclude by discussing how the average potential and kinetic energies are no longer equal in the presence of shear.

Initial surface disturbance on a shear current: The Cauchy-Poisson problem with a twist

We solve for the first time the classical linear Cauchy-Poisson problem—the time evolution of an initial surface disturbance—when a shear current of uniform vorticity is present beneath the surface. The solution is general, including the effects of gravity, surface tension, and constant finite depth. The particular case of an initially Gaussian disturbance of width b is studied for different values of three system parameters: a “shear Froude number” Sb/g (S is the vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well-known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are anal...

Electrostrictive fluid pressure from a laser beam

Recent times have seen a surge of research activity on systems combining fluid mechanics and electromagnetic fields. In radiation optics, whenever information about the distribution of pressure in a dielectric fluid is required, the contribution from electrostriction becomes important. In the present paper, we calculate how the local pressure varies with position and time when a laser beam is imposed in a uniform fluid. A Gaussian intensity profile of arbitrary time dependence is assumed for the beam, and general results are derived in this case. For demonstration, we analyze two different cases: first, that the beam is imposed suddenly (mathematically in the form of a step function) and second, that the beam is switched on in a soft way. In both cases, simple analytical expressions for the pressure distribution are found.

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current [Ellingsen, J.~Fluid Mech.\ {\bf 742} R2 (2014)]. We derive the exact criterion for criticality as a function of an intrinsic shear Froude number

Temperature-independent Casimir-Polder forces despite large thermal photon numbers.

S\sqrt{b/g}

Casimir effect at nonzero temperature for wedges and cylinders

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