Narrow Results

The plausible resolution of the Casimir puzzle implying that the dissipative Drude model is not applicable in the area of transverse electric evanescent waves is discussed. Calculations show that for the propagating waves, as well for the evanescent waves with transverse magnetic polarization, the Drude model can be used in calculations of the Casimir force by the Lifshitz theory with no contradictions with the measurement data. The lateral component of magnetic field of the magnetic dipole oscillating near a metallic surface is computed for the parameters of experiment in preparation which is aimed to directly check the validity of the Drude model in the area of transverse electric evanescent waves. By comparing with the case of graphene, whose dielectric response is spatially nonlocal and possesses the double pole at zero frequency, it is hypothesized that the success of the dissipationless plasma model in this area is also caused by the presence of a double pole.

In this paper, we consider the Casfimir effect in a (1+1)-dimensional model with a critical mode. Such a mode gives rise to a condensate described by the nonlinear Gross–Pitaevskii equation. In the condensate, there are two sources of the Casimir force; one is the conventional one resulting from the fluctuations, the other follows from the condensate. We consider three simple models that allow for condensate solutions in terms of elliptic Jacobi functions. We also investigate a method for obtaining approximate solutions and show its range of applicability. In all three examples, we compute the condensate energy. In one example with a finite interval with Robin boundary conditions on one side and Dirichlet conditions on the other side, we calculate the vacuum energy and the Casimir force. There is a competition between the forces from the condensate and the fluctuations. We mention that the force from the condensate is always repulsive.

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ³ to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.

The Casimir force on two-dimensional pistons for massive scalar fields with both Dirichlet and hybrid boundary conditions is computed. The physical result is obtained by making use of generalized ζ-function regularization technique. The influence of the mass and the position of the piston in the force is studied graphically. The Casimir force for massive scalar field is compared to that for massless scalar field.

In this paper we study the Casimir force for a piston configuration in R³ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in R³ and for possible modifications from extra dimensional manifolds.

Charged massive matter fields of spin-0 and spin-$\frac{1}{2}$ are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.

In an attempt to explain some of the unknown phenomena of nature, including dark energy and dark matter, we explore the possibility of the existence of a fifth fundamental force of nature as also cited by some researchers. With the inclusion of such a force in the system, some of the vague things can be explained and there is high hope of its importance in building up a “theory of everything”. With this intention, we investigate some manifestations of the fifth force which stand from theoretical calculations or from theoretical point of view, though till now there is less experimental proof. However, the theoretical results obtained indicate the existence of a fifth force which will lead to the completion in defining the laws of physics and nature. With this discovery, science may be able to explain the whole complexity of the Universe in near future.

Contaminants on the boundary surfaces lead to electric potential inhomogeneities. The resulting poorly defined electric force leads to ambiguities in precision Casimir force measurements. We experimentally demonstrate that with UV light followed by Ar ion beam radiation the electrostatic effects from these patch potentials can be eliminated. The cleaning procedure discussed reduces the sphere-plate potential difference to near zero. In addition, the UV radiation results in vacuum chamber pressures being reduced by a factor of 10 from the removal of volatile molecular species. This leads to very stable and near zero sphere-plate potential differences. The reported combination UV and Ar ion in situ cleaning procedure will find wide application.

Many precision experiments have been done in the Casimir regime and in short range gravity when the separation between the interacting bodies is in the sub-micron range. Experimental complexity is minimized when one of the bodies is a sphere and the other one is a plate, making the alignment between the two bodies ubiquitous. Our group has produced the most precise Casimir measurements, and the best limits on predicted Yukawa-like potentials by measuring a force between a $R\sim 150\mu \mathrm{\text{m}}$ sphere attached to a ${(500\mu \mathrm{\text{m}})}^2$ micro-mechanical oscillator and a planar source mass. By replacing the spherical surface with a fraction of a $500\mu \mathrm{\text{m}}$ long cylinder with $R\sim 150\mu$m, the force sensitivity can be greatly enhanced. Here, it is paramount to know the angular deviation between the long axis of the cylinder and both the axis of rotation of the oscillator and the plate. Tests between a cylinder and a structure etched into a silicon wafer show that deviations of $20\mu$rad are readily accessible. Additionally, a scaled up experiment is used to investigate if capacitance measurements can determine the orientation of the cylinder with respect to a plane with the required precision.

The dependence of the Casimir force on the optical properties and geometry of interacting materials makes possible to tailor the actuation dynamics of micro/nano actuators. In this research, we study the dynamical sensitivity of micro- and nanoelectromechanical systems on geometry by comparing the plate-plate and sphere-plate configurations, and taking into account the optical properties of the interacting materials. In fact, for conservative systems bifurcation analysis and phase portraits show that the geometry and the optical properties strongly influence the stability of an actuating device in a way that geometries that lead to weaker Casimir forces (sphere-plate geometry) favor more stable behavior. In addition, for non-conservative periodically driven systems, the Melnikov and Poincare portrait analysis shows that stronger Casimir forces lead to increased chaotic behavior, which more pronounced for the plate-plate geometry, that prohibits the long term prediction of the actuating dynamics of the system.

Casimir interaction of two SiO₂ glass half spaces being substrates for Chern-Simons boundary layers is studied. The separation between two half spaces at which the Casimir energy minimum occurs is strongly increased for dielectric SiO₂ glass substrates in comparison with previously considered metal Au and semiconductor Si substrates. Strong reduction in the Casimir force due to presence of Chern-Simons layers is found for SiO₂ glass substrate. Influence of modification of the infrared absorption on the Casimir force is studied.

We investigate the Casimir pressure between two dissimilar plates separated by a layer of magnetic fluid. Numerical computations of the Casimir pressure are performed for Au and SiO₂ plates with an intervening layer of water and water-based ferrofluid obtained on addition to water a 5% volume fraction of magnetite nanoparticles with 10 nm diameter. It is shown that an addition of nanoparticles leads to a widening of separation region, where the Casimir interaction is repulsive. This result does not depend on whether the plasma or the Drude model is used for extrapolation of the optical data of Au to low frequencies. The effect of enhanced repulsion due to the presence of ferrofluid may be useful for preventing stiction of closely spaced elements in various microdevices.

We explore the impact of a sudden shift in the mass of a scalar boson field on long-range forces mediated by this field under the framework of unitarily inequivalent vacua. Since the search for new long-range forces is an active experimental area probing physics beyond the Standard Model, the consequence of a non-trivial vacuum state of a scalar boson on these experiments is elucidated. We show that while the mass shift affects the one-boson exchange potential, the Casimir force remains only dependent on the vacuum state.

Constraints on the Yukawa-type long-range interactions following from the Casimir effect are considered. The constraints obtained from the recent Casimir force measurements by means of a torsion pendulum and an atomic force microscope are collected and compared. New constraints are obtained from the measurement of the lateral Casimir force. The conclusion is made that the Casimir effect has an advantage over the conventional methods in obtaining stronger constraints on hypothetical interactions.

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.

We have performed a precise experimental determination of the Casimir pressure between two gold-coated parallel plates by means of a micromachined oscillator. In contrast to all previous experiments on the Casimir effect, where a small relative error (varying from 1% to 15%) was achieved only at the shortest separation, our smallest experimental error (~ 0.5%) is achieved over a wide separation range from 170 nm to 300 nm at 95% confidence. We have formulated a rigorous metrological procedure for the comparison of experiment and theory without resorting to the previously used root-mean-square deviation, which has been criticized in the literature. This enables us to discriminate among different competing theories of the thermal Casimir force, and to resolve a thermodynamic puzzle arising from the application of Lifshitz theory to real metals. Our results lead to a more rigorous approach for obtaining constraints on hypothetical long-range interactions predicted by extra-dimensional physics and other extensions of the Standard Model. In particular, the constraints on non-Newtonian gravity are strengthened by up to a factor of 20 in a wide interaction range at 95% confidence.

Modern unification theories that seek to unify gravity with the other fundamental forces predict a host of new particles outside the standard model. Many also invoke extra dimensions. Both of these effects lead to deviations from Newtonian gravity. For sub micron distance between two bodies, the Casimir force far exceeds the gravitational force. Thus both understanding and using the Casimir force is very important for checking the relevance of these unification theories. In particular, measurements of the Casimir force has allowed one to set some of the strongest constraints for corresponding distance regions. This paper summarizes the techniques used to measure the Casimir force and some of the limits that follow from them.

We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivity of dielectric plates is proved to lead to a violation of the Nernst heat theorem and, thus, is not related to the phenomenon of dispersion forces. The low-temperature asymptotics of the Casimir free energy, pressure and entropy are derived also in the configuration of one metal and one dielectric plate. The results are shown to be consistent with thermodynamics if the dielectric plate possesses a finite static dielectric permittivity. If the dc conductivity of a dielectric plate is taken into account this results in the violation of the Nernst heat theorem. We discuss both the experimental and theoretical results related to the Casimir interaction between metal and semiconductor with different charge carrier density. Discussions in the literature on the possible influence of spatial dispersion on the thermal Casimir force are analyzed. In conclusion, the conventional Lifshitz theory taking into account only the frequency dispersion remains the reliable foundation for the interpretation of all present experiments.

The Lifshitz theory of dispersion forces leads to thermodynamic and experimental inconsistencies when the role of drifting charge carriers is included in the model of the dielectric response. Recently modified reflection coefficients were suggested that take into account screening effects and diffusion currents. We demonstrate that this theoretical approach leads to a violation of the third law of thermodynamics (Nernst's heat theorem) for a wide class of materials and is excluded by the data from two recent experiments. The physical reason for its failure is explained by the violation of thermal equilibrium, which is the fundamental applicability condition of the Lifshitz theory, in the presence of drift and diffusion currents.

Experimental procedures associated with the electrostatic calibration of a microelectromechanical torsional oscillator are reported. These calibrations are required for the precision measurements of the Casimir force between a Au-coated sapphire sphere and a Au-coated polysilicon plate. It is shown that the electrostatic force between the surfaces is made zero by the application of a potential difference V_o between the sphere and the plate. V_o is found to be independent of position and separation within the experimental error.