A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

Casimir force in dense confined electrolytes

ABSTRACT

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.     

On the dynamic instability of nanowire-fabricated electromechanical actuators in the Casimir regime: Coupled effects of surface energy and size dependency

Herein, the dynamic pull-in instability of cantilever nanoactuator fabricated from conductive cylindrical nanowire with circular cross-section is studied under the presence of Casimir force. The Gurtin–Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and size phenomenon. Using Green–Lagrange strain, the higher order surface stress components are incorporated in the governing equation. The Dirichlet mode is considered and an asymptotic solution, based on the path integral approach, is applied to consider the effect of the Casimir attraction. Furthermore, the influence of structural damping is considered in the model. The nonlinear governing equation is solved using analytical reduced order method (ROM). The effects of various parameters on the dynamic pull-in parameters, phase planes and stability threshold of the actuator are demonstrated.     

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.     

Experimental investigation of the Casimir force beyond the proximity-force approximation

The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z<300 nm, we find that the magnitude of the fractional deviation from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0.4z/R, where R is the radius of the sphere.     

The forces on a single interacting Bose–Einstein condensate

Using double parabola approximation for a single Bose–Einstein condensate confined between double slabs we proved that in grand canonical ensemble (GCE) the ground state with Robin boundary condition (BC) is favored, whereas in canonical ensemble (CE) our system undergoes from ground state with Robin BC to the one with Dirichlet BC in small-L region and vice versa for large-L region and phase transition in space of the ground state is the first order. The surface tension force and Casimir force are also considered in both CE and GCE in detail.     

Instability threshold of rippled carbon nanotube nanotweezers in the low vacuum gas flow incorporating Dirichlet and Neumann modes of Casimir energy

The aim of this research work is to address the influences of dispersion forces and rippled configuration on the instability threshold of carbon nanotube (CNT) based nanotweezers. To this end, the Dirichlet and Neumann modes of Casimir force arisen from the electric and magnetic energies is developed for cylinder–cylinder geometry. Moreover, the CNTs rippling deformation which experimentally revealed is included in the Euler-Bernoulli beam model to modify the governing equations. The differential quadrature method (DQM) in conjunction with the 4th-order Runge-Kutta algorithm is employed to numerically simulate the non-linear partial differential equations. It is interestingly demonstrated that these phenomena remarkably affect the electromechanical behavior of nanotweezers fabricated from CNTs. By taking the rippling configuration and Casimir attraction between tubes into account, the pull-in voltage decreases. On the other hand, when the gas damping effect due to low vacuum environment is taken into consideration, the pull-in value increases. The accuracy of the present modeling is compared with those experimentally published in the literature, giving excellent results.     

Casimir force on a surface with shallow nanoscale corrugations: geometry and finite conductivity effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.     

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.     

Casimir Force in a One-Dimensional Cavity with Quasimode

We calculate the Casimir force between a perfect reflective wall and a semitransparent wall in the laser cavity. Using the Fox-Li quasimode theory to describe the electromagnetic field in the laser cavity, the vacuum energy and the Casimir force are calculated. We compare our results to the force in the ideal situation and find it smaller in the dissipative cavity. We also find that the Casimir force decreases with the increase of the wall-wall distance and the decay rate of the quasimodes in the laser cavity.     

Chiral Anomaly-Enhanced Casimir Interaction between Weyl Semimetals

We theoretically study the Casimir interaction between Weyl semimetals.When the distance a between semiinfinite Weyl semimetals is in the micrometer regime,the Casimir attraction can be enhanced by the chiral anomaly.The Casimir attraction depends sensitively on the relative orientations between the separations(b_1,b_2)of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations(b_1,b_2) when they orient parallel to the interface.This anisotropy is quite larger than that in conventional birefringent materials.The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations(b_1,b_2) is perpendicular to the interface.The Casimir attraction between Weyl semimetal slabs decays slower than 1/a4 when the Weyl nodes separations b_1 and b_2 are both parallel to the interface.     

Nonequilibrium 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 nonequilibrium 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.     

Amplification phenomena of Casimir force fluctuations on close scatterers coupled via a coherent fermionic fluid

We study the mechanical actions affecting close scatterers immersed in a coherent fermionic fluid. Using a scattering field theory, we theoretically analyse the single-scatterer and the two-scatterer case. Concerning the single-scatterer case, we find that a net force affects the scatterer dynamics only in non-equilibrium condition, i.e. imposing the presence of a non-vanishing particle current flowing through the system. The force fluctuation (variance) is instead not negligible both in equilibrium and in non-equilibrium conditions. Concerning the two-scatterer case, an attractive fluid-mediated Casimir force is experienced by the scatterers at small spatial separation, while a decaying attractive/repulsive behavior as a function of the scatterer separation is found. Furthermore, the Casimir force fluctuations acting on a given scatterer in close vicinity of the other present an oscillating behavior reaching a long distance limit comparable to the noise level of the single-scatterer case. The relevance of these findings is discussed in connection with fluctuation phenomena in low-dimensional nanostructures and cold atoms systems.     

卡西米尔力

量子电动力学中的卡西米尔力是真空零点能的体现.广义的卡西米尔力则依赖于涨落介质的类型广泛地出现于物理中,包括量子,临界,戈德斯通模,以及非平衡卡西米尔力.长程关联的涨落介质和约束是产生卡西米尔力的两个条件.本文通过回顾卡西米尔物理的发展,讨论了不同类型的卡西米尔力,几种正规化方法,并对卡西米尔物理的进一步发展做了展望.     

On the ponderomotive force and the effect of loss reaction on parametric instability

In this paper, the growth rate, ponderomotive force and the exciting condition for parametric instability are derived by considering the loss reaction using a new method. On the basis of the hydrodynamic equations, we take the production and loss reactions in plasma into account to derive the coupling equations for the electron plasma oscillation and ion acoustic oscillation, and obtain the growth rate for the parametric instability, the ponderomotive force and the exciting condition. The result shows that (a) the production reaction has no effect on the parametric instability, and the effect of loss reaction on the parametric instability is a damping one, (b) the more intensive the external field or pump is, the larger the growth rate is, (c) there exist two modes of the ponderomotive force, i.e.\ the high frequency mode and the low frequency mode, and (d) when ponderomotive force counteracts the damping force, the oscillations become non-damping and non-driving. The ratio of the electron plasma oscillation to ion acoustic oscillation is independent of the loss reaction and the external field.     

The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions

The Casimir effect for parallel plates in the presence of compactified universal extra dimensions within the frame of Kaluza–Klein theory is analyzed. Having regularized and discussed the expressions of Casimir force in the limit, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough and the higher-dimensional spacetime is, the greater the value of repulsive Casimir force between plates is. The repulsive nature of the force is not consistent with the experimental phenomena.     

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.     

Forces between conducting surfaces due to spatial variations of surface potential

We describe analytical and numerical methods for calculating forces between conductors due to variations of electrostatic surface potential across their surfaces. In the simple case where the spatial variation of surface potential gives rise to uniform power spectra, we show that the electrostatic force can be large in comparison with, and scale in approximately the same way with distance of closest approach as, the Casimir force. Patch potentials that are consistent with existing experimental data could give rise to forces with a magnitude of 4% of the Casimir force at separations of 0.1 microm.     

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using full quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.