Thermal Casimir effect in ideal metal rectangular boxes

The thermal Casimir effect in ideal metal rectangular boxes is considered using the method of zeta functional regularization. A renormalization procedure is suggested which provides the finite expression for the Casimir free energy in any restricted quantization volume. This expression satisfies the classical limit at high temperature and leads to zero thermal Casimir force for systems with infinite characteristic dimensions. In the case of two parallel ideal metal planes the results, as derived previously using thermal quantum field theory in Matsubara formulation and other methods, are reproduced starting from the expression obtained. It is shown that for rectangular boxes the temperature-dependent contribution to the electromagnetic Casimir force can be both positive and negative depending on side lengths. Numerical computations of the scalar and electromagnetic Casimir free energy and force are performed for cubes.     

Effect of the electric current on the Casimir force between graphene sheets

The dependence of the thermal component of the Casimir force and Casimir friction between graphene sheets on the drift velocity of charge carriers in one of the sheets has been analyzed. It has been shown that the drift motion results in the measurable change in the thermal Casimir force owing to the Doppler effect. The thermal Casimir force, as well as Casimir friction, increases strongly in the case of resonant photon tunneling, when the energy of an emitted photon coincides with the excitation energy of an electron-hole pair. In the case of resonant photon tunneling, the dominant contribution to the Casimir friction even at temperatures above room temperature comes from quantum friction caused by quantum fluctuations. Quantum friction can be detected in an experiment on the friction drag between graphene sheets in a high electric field.     

The Casimir Effect at Finite Temperature in a Six-Dimensional Vortex Scenario

The Casimir effect for parallel plates satisfying the Dirichlet boundary condition in the context of effective QED coming from a six-dimensional Nielsen-Olesen vortex solution of the Abelian Higgs model with fermions coupled to gravity is studied at finite temperature. We find that the sign of the Casimir energy remains negative under the thermal influence. It is also shown that the Casimir force between plates will be weaker in the higher-temperature surroundings while keeps attractive. This Casimir effect involving the thermal influence is still inconsistent with the known experiments. We find that the thermal correction can not compensate or even reduce the modification from this kind of vortex model to make the Casimir force to be in less conflict with the measurements.     

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.     

Experiment and theory in the Casimir effect

Casimir effect is the attractive force which acts between two plane parallel, closely spaced, uncharged, metallic plates in vacuum. This phenomenon was predicted theoretically in 1948 and reliably investigated experimentally only in recent years. In fact, the Casimir force is similar to the familiar van der Waals force in the case of relatively large separations when the relativistic effects come into play. We review the most important experiments on measuring the Casimir force by means of torsion pendulum, atomic force microscope and micromechanical torsional oscillator. Special attention is paid to the puzzle of the thermal Casimir force, i.e. to the apparent violation of the third law of thermodynamics when the Lifshitz theory of dispersion forces is applied to real metals. Thereafter we discuss the role of the Casimir force in nanosystems including the stiction phenomenon, actuators, and interaction of hydrogen atoms with carbon nanotubes. The applications of the Casimir effect for constraining predictions of extra-dimensional unification schemes and other physics beyond the standard model are also considered.     

Finite-temperature Casimir effect in piston geometry and its classical limit

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with perfect electric-conductor and perfect magnetic-conductor boundary conditions. The Casimir energy in a rectangular cavity is derived using the cut-off method. It is shown that the divergent part of the Casimir energy does not contribute to the Casimir force acting on the piston, thus renders an unambiguously defined Casimir force acting on the piston. At any temperature, it is found that the Casimir force acting on the piston increases from −∞ to 0 when the separation a between the piston and the opposite wall increases from 0 to ∞. This implies that the Casimir force is always an attractive force pulling the piston towards the closer wall, and the magnitude of the force gets larger as the separation a gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan–Boltzmann (or black-body radiation) term which is of order T ^d+1, it is found that the contributions of this term from the two regions separating the piston cancel with each other in the case of piston. The high-temperature leading-order term of the Casimir force acting on the piston is of order T, which shows that the Casimir force has a nontrivial classical ℏ→0 limit. Explicit formulas for the classical limit are computed.     

Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect

We present supplementary information on the recent indirect measurement of the Casimir pressure between two parallel plates using a micromachined oscillator. The equivalent pressure between the plates is obtained by means of the proximity force approximation after measuring the force gradient between a gold coated sphere and a gold coated plate. The data are compared with a new theoretical approach to the thermal Casimir force based on the use of the Lifshitz formula, combined with a generalized plasma-like dielectric permittivity that takes into account interband transitions of core electrons. The theoretical Casimir pressures calculated using the new approach are compared with those computed in the framework of the previously used impedance approach and also with the Drude model approach. The latter is shown to be excluded by the data at a 99.9% confidence level within the wide separation range from 210 to 620 nm. The level of agreement between the data and theoretical approaches based on the generalized plasma model, or the Leontovich surface impedance, is used to set stronger constraints on the Yukawa forces predicted from the exchange of light elementary particles and/or extra-dimensional physics. The resulting constraints are the strongest in the interaction region from 20 to 86 nm with a largest improvement by a factor of 4.4 at 26 nm.     

Noncontact racK and pinion powered by the lateral Casimir force

The lateral Casimir force is employed to propose a design for a potentially wear-proof rack and pinion with no contact, which can be miniaturized to the nanoscale. The robustness of the design is studied by exploring the relation between the pinion velocity and the rack velocity in the different domains of the parameter space. The effects of friction and added external load are also examined. It is shown that the device can hold up extremely high velocities, unlike what the general perception of the Casimir force as a weak interaction might suggest.     

Three-dimensional Casimir piston for massive scalar fields

We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a⁴ when a→0⁺ and decays exponentially when a→∞. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.     

A theory of electromagnetic fluctuations for metallic surfaces and van der waals interactions between metallic bodies

A new general expression is derived for the fluctuating electromagnetic field outside a metal surface in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between dielectric solids. The theory is used to compute the radiative heat transfer between two parallel metal surfaces at different temperatures. It is shown that a measurement of this quantity may provide an experimental resolution of a long-standing controversy about the effect of thermal corrections on the Casimir force between real metal plates.     

Casimir friction force between a SiO<Subscript>2</Subscript> probe and a graphene-coated SiO<Subscript>2</Subscript> substrate

The possibility of mechanical detection of Casimir friction with the use of a noncontact atomic force microscope is discussed. A SiO₂ probe tip located above a graphene-coated SiO₂ substrate is subjected to the frictional force caused by a fluctuating electromagnetic field produced by a current in graphene. This frictional force will create the bend of a cantilever, which can be measured by a modern noncontact atomic force microscope. Both the quantum and thermal contributions to the Casimir frictional force can be measured using this experimental setup. This result can also be used to mechanically detect Casimir friction in micro- and nanoelectromechanical systems.     

Long-range magnetic interaction due to the Casimir effect

The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to decay as D-1 in the limit of short distances, and as D-5 in the limit of long distances. Explicit expressions for realistic systems are given in the large- and small-distance limits. An experimental test of the Casimir magnetic interaction is proposed.     

Anomalous temperature dependence of the Casimir force for thin metal films

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.     

A verification of quantum field theory — measurement of Casimir force

Here we review our work on measurement of the Casimir force between a large aluminum coated a sphere and flat plate using an atomic force microscope. The average statistical precision is 1% of the force measured at the closest separation. We have also shown nontrival boundary dependence of the Casimir force.     

Repulsive Casimir forces

We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.     

Vortex fluctuations in the critical Casimir effect of superfluid and superconducting films

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when the size of the thermal vortex loops is comparable to the film thickness, and the results for TT(c). When applied to a high-T(c) superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and the bulk, and estimates show that this may be readily measurable.     

Casimir force pressure on the insulating layer in metal-insulator-semiconductor structures

The Casimir force pressure on the insulating layer in metal-insulator-semiconductor structures with parameters close to those used in the production of semiconductor devices has been calculated. It has been shown that the Casimir force pressure increases tenfold and reaches several tens of pascals as the insulator thickness decreases from 80 to 40 nm. The metal layer thickness and the presence of the surface layer with a high charge carrier concentration in the semiconductor have a slight effect on calculated values of the Casimir pressure.     

Demonstration of the lateral casimir force

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to 0.3 microm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.     

Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

In this work we investigate the influence of the combined effect from random self-affine roughness, finite conductivity, and finite temperature on the pull-in voltage in microswitches influenced by thermal and quantum vacuum fluctuations through the Casimir force and electrostatic forces. It is shown that for separations within the micron or sub-micron range the roughness influence plays a dominant role, while temperature starts to show its influence well above micron separations. Indeed, increasing the temperature leads to higher pull-in voltages since it leads to an increased Casimir force. The temperature influence is more significant for relatively large roughness exponent H ∼ 1, while its influence is significantly lower with increasing lateral roughness correlation length ξ or due to long wavelength surface smoothness.