Casimir Effect Research Articles

Casimir effect, loop corrections, and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions

Casimir effect, loop corrections, and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions

Axion electrodynamics: Green’s functions, zero-point energy and optical activity

Starting from the theory of Axion Electrodynamics, we work out the axionic modifications to the electromagnetic Casimir energy using the Green’s function method, both when the axion field is initially assumed purely time-dependent and when the axion field configuration is a static domain wall, so purely space-dependent. For the first case it means that the oscillating axion background is taken to resemble an axion fluid at rest in a conventional Casimir setup with two infinite parallel conducting plates, while in the second case we evaluate the radiation pressure acting on an axion domain wall. We extend previous theories in order to include finite temperatures. Various applications are discussed. (i) We review the theory of Axion Electrodynamics and particularly the energy–momentum conservation in a linear dielectric and magnetic material. We treat this last aspect by extending former results by Brevik and Chaichian (2022) and Patkos (2022). (ii) Adopting the model of the oscillating axion background we discuss the axion-induced modifications to the Casimir force between two parallel plates by using the Green’s function method. (iii) We calculate the radiation pressure acting on an axion domain wall at finite temperature T. Our results for an oscillating axion field and a domain wall are also useful for condensed matter physics, where some topological materials, “axionic topological insulators”, interact with the electromagnetic field with a Chern–Simons interaction, like the one in Axion Electrodynamics, and there are experimental systems analogous to time-dependent axion fields and domain walls as the ones showed e.g. by Jiang and Wilczek (2019) and Fukushima et al. (2019). (iv) We compare our results, where we assume time-dependent or space-dependent axion configurations, with the discussion of the optical activity of Axion Electrodynamics by Sikivie (2021) and Carrol et al. (1990). We also make comparisons with the properties of known materials, such as optically active, chiral media and the Faraday effect.

Remnants of the nonrelativistic Casimir effect on the lattice

The Casimir effect is a fundamental quantum phenomenon induced by the zero-point energy for a quantum field. It is well-known for relativistic fields with a linear dispersion relation, while its existence or absence for nonrelativistic fields with a quadratic dispersion is an unsettled question. Here, we investigate the Casimir effects for various dispersion relations on the lattice. We find that Casimir effects for dispersions proportional to an even power of momentum are absent in a long distance but a remnant of the Casimir effect survives in a short distance. Such a remnant Casimir effect will be experimentally observed in materials with quantum fields on the lattice, such as thin films, narrow nanoribbons, and short nanowires. In terms of this effect, we also give a reinterpretation of the Casimir effect for massive fields.

Imprints of Casimir wormhole in Einstein Gauss–Bonnet gravity with non-vanishing complexity factor

This article investigates Casimir wormhole solutions in Einstein Gauss–Bonnet (EGB) gravity. We are familiar that Null energy conditions (NEC) need not be satisfied for a stable wormhole due to the existence of exotic matter. As the Casimir effect acts as a negative energy source, it can be treated as a classical applicant for the exotic matter to discuss the stable dynamics of the wormhole. This work explores the Casimir effects with the Generalized Uncertainty Principle (GUP) on wormhole geometry in EGB gravity by confining our results for D=5. We have examined two GUP procedures, e.g., Kempf, Mangano, Mann (KMM) and Dentournay, Gabriel, and Spindel (DGS). We have developed shape functions for Casimir wormholes, and GUP corrected Casimir wormholes and studied their existence. In addition, we investigate the behavior of the Gauss–Bonnet (GB) Coupled parameter and minimal uncertainty (MU) parameter on the Equation of state (EOS) parameter. The active gravitational mass and embedding diagrams for all developed shape functions are analysed. Moreover, the violation of the NEC by an exotic matter, the equilibrium forces, and the complexity factor of Casimir wormholes and GUP-corrected Casimir wormholes have also been explored.

Quantum friction in the presence of a perfectly conducting plate

A neutral but polarizable particle at rest near a perfectly conducting plate feels a force normal to the surface of the plate, which tends to pull the particle towards the plate. This is the well-known Casimir-Polder force, which has long been theoretically proposed and experimentally observed. In this paper, we explore the transverse frictional force on an atom moving uniformly parallel to a perfectly conducting plate. Although many theoretical predictions can be found for the quantum friction on a particle moving above an imperfect surface, the extreme situation with a perfectly conducting plate seems to have been largely unaddressed by the theoretical community. We investigate this ideal case as a natural extension of our previous work on quantum vacuum friction, and conclude that there does exist a quantum frictional force on an atom moving above a perfectly conducting plate, which we will abbreviate by PCQF. Like quantum vacuum friction, PCQF arises from the interaction between the particle and the surrounding blackbody radiation. But, the behavior of PCQF differs from the quantum vacuum friction in that the vacuum fields are modified by the perfectly conducting plate. Very interestingly, the distance dependence, the temperature dependence, and even the sign of the frictional force can depend on the polarization state of the atom. For an isotropic atom with a static polarizability, the resultant frictional force is found to be negative definite and therefore remains a true drag. Just above the surface of the plate, the magnitude of the frictional force is twice that of the quantum vacuum friction in the absence of the plate.

Dirac/Weyl-node-induced oscillating Casimir effect

The Casimir effect is a quantum phenomenon induced by the zero-point energy of relativistic fields confined in a finite-size system. This effect for photon fields has been studied for a long time, while the realization of counterparts for fermion fields in Dirac/Weyl semimetals is an open question. We theoretically demonstrate the typical properties of the Casimir effect for relativistic electron fields in Dirac/Weyl semimetals and show the results from an effective Hamiltonian for realistic materials such as Cd3As2 and Na3Bi. We find an oscillation of the Casimir energy as a function of the thickness of the thin film, which stems from the existence of Dirac/Weyl nodes in momentum space. Experimentally, such an effect can be observed in thin films of semimetals, where the thickness dependence of thermodynamic quantities is affected by the Casimir energy.

Effect of flexoelectricity on the Pull-in instability of beam-type NEMS

Considering the increasing number of smart materials in advanced industries and technologies, the need to investigate the use of these materials is felt more and more. The flexoelectric effect is one of the most important phenomena created in micro-scale beams, which will have a significant effect on the results and should be investigated. Therefore, in this article, the Pull-in instability in the beam-type microelectromechanical systems has been investigated under the flexoelectric effect. The governing equations of the system have been derived based on the theory that is founded on the strain gradient theory for the Euler-Bernoulli beam model. This beam is under the effect of intermolecular Casimir force and electrostatic force. The equations and boundary conditions related to them have been non-dimensionalized first in direct and indirect flexoelectric effect. With the help of the differential quadrature method, the Pull-in voltage's critical parameters and the system's free-standing behavior have been studied. Among the significant results obtained from this research, it is possible to mention the Pull-in voltage increase due to the flexoelectric effect reduction. Also, in the indirect state of the flexoelectric effect, the increase in the initial applied voltage causes a decrease in the Pull-in voltage.

Investigating Casimir effect in sonoluminescence bubble: A brief overview

The focus of our investigation is the feasibility of examining the Casimir effect in a spherically symmetric sonoluminescence bubble. Our recommendations are based on an in-depth analysis of the relevant literature and experimental data. To forecast the expansion time of the bubble under irradiated shock waves, we primarily relied on Schwinger calculations. Furthermore, we addressed the inconsistencies associated with the failure to link sonoluminescence (SL) with the Casimir effect. Our findings indicate that SL is a highly delicate and reliant metric, with its measurement relying on variables such as the type of gas used to produce the bubble, fluid and gas temperatures, surface tension, density, pressure, and radius. Based on our analysis, we conclude by proposing adjustments to various gases, particularly at different temperatures, to accurately assess SL using Casimir forces and energy. We believe that our study will aid in the acceleration of future investigations into precisely measuring SL bubbles.

Casimir effect for a stack of graphene sheets

We consider a stack of parallel sheets composed of conducting planes with tensorial conductivities. Using the scattering matrix approach, we derive explicit formulas for the Casimir energy of two, three, and four planes as well as a recurrence relation for arbitrary planes. Specifically, for a stack of graphene, we solve the recurrence relations and obtain formulas for the Casimir energy and force acting on the planes within the stack. Moreover, we calculate the binding energy in the graphene stack with graphite interplane separation, which amounts to ${E}_{ib}=9.9$ meV/atom. Notably, the Casimir force on graphene sheets decreases rapidly for planes beyond the first one. For the second graphene layer in the stack, the force is 35 times smaller than that experienced by the first layer.

The Casimir effect in a dilute Bose gas at zero-temperature taking into account the contribution of self-energy within CJT theory

The Casimir effect in a weakly interacting Bose-Einstein condensate (BEC) gas is investigated at zero temperature within the Cornwall-Jackiw-Tomboulis (CJT) effective action approach under elastic and twisted boundary conditions (BCs) of the wave vector. After discussing the rationales for applying the CJT theory to a confinement BEC system, we establish the analytical formulae and then evaluate the numerical values of the Casimir force, which are essential for the observation experiment of the theoretical results.

Traversable wormhole models supported by a string cloud in rainbow gravity

The traversable wormholes are fascinating as the shortcuts in space–time. This work discusses the geometry of a traversable wormhole with a string cloud as a source in rainbow gravity. The field equations are developed and solved to obtain the wormhole’s shape function, cloud’s mass density, and string tension. We have calculated the shape function and made it specific to study the dynamics for toy model. Based on the three well-known pairs of rainbow functions (mentioned by Ali and Khalil), the string cloud’s dynamical variables including mass density and string tension are graphically presented. The corresponding energy conditions are also visually depicted. It is found that the source matter (string cloud) of the traversable wormhole must be exotic. However, the positive values of the string tension led to the presence of Casimir and dark energy effects. It is found that the toy model respects the null energy condition for a single pair of rainbow functions, i.e., Rainbow Function Type II. We have concluded that in rainbow gravity theory, the traversable wormhole solutions originating from a string cloud requires the presence of exotic matter to achieve a stable structure.

Fluctuation-induced dispersion forces on thin DNA films.

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Casimir energy for spinor fields with δ-shell potentials

This work analyzes the Casimir energy of a massive spinor field propagating in flat space endowed with a spherically symmetric δ-function potential. By utilizing the spectral zeta function regularization method, the Casimir energy is evaluated after performing a suitable analytic continuation. Explicit numerical results are provided for specific cases in which the Casimir energy is unambiguously defined. The results described in this work represent a generalization of the MIT bag model for spinor fields.

Dynamical atom-wall Casimir-Polder effect after a sudden change of the atomic position

We investigate the dynamical Casimir-Polder force between an atom and a conducting wall during the time evolution of the system from a partially dressed state. This state is obtained by a sudden change of the atomic position with respect to the plate. To evaluate the time-dependent atom-plate Casimir-Polder force we solve the Heisenberg equations for the field and atomic operators by an iterative technique. We find that the dynamical atom-plate Casimir-Polder interaction exhibits oscillation in time, and can be attractive or repulsive depending on time and the atom-wall distance. We also investigate the time dependence of global observables, such as the field and atomic Hamiltonians, and discuss some interesting features of the dynamical process bringing the interaction energy to the equilibrium configuration.

Field observables near a fluctuating boundary

We review several aspects related to the confinement of a massless scalar field in a cavity with a movable conducting wall of finite mass, free to move around its equilibrium position to which it is bound by a harmonic potential, and whose mechanical degrees of freedom are described quantum mechanically. This system, for small displacements of the movable wall from its equilibrium position, can be described by an effective interaction Hamiltonian between the field and the mirror, quadratic in the field operators and linear in the mirror operators. In the interacting, i.e. dressed, ground state, we first consider local field observables such as the field energy density: we evaluate changes of the field energy density in the cavity with the movable wall with respect to the case of a fixed wall, and corrections to the usual Casimir forces between the two walls. We then investigate the case of two one-dimensional cavities separated by a movable wall of finite mass, with two massless scalar fields defined in the two cavities. We show that in this case correlations between the squared fields in the two cavities exist, mediated by the movable wall, at variance with the fixed-wall case.

The Casimir Effect for Diffraction Gratings, Symmetry Breaking, and Geometric Transitions

The Casimir Effect for Diffraction Gratings, Symmetry Breaking, and Geometric Transitions

Classicality of the Bogoliubov Transformations and the Dynamical Casimir Effect Through the Reduced State of the Field

We use the reduced state of the field formalism [Entropy 21, 705 (2019)] to derive conditions under which a Bogoliubov transformation can be considered semi-classical. We apply this result to the dynamical Casimir effect in a moving medium [Phys. Rev. A 78, 042109 (2008)], discussing its classical and quantum features.

Bosonic Casimir Effect in an Aether-like Lorentz-Violating Scenario with Higher Order Derivatives

In this paper, we investigate the bosonic Casimir effect in a Lorentz-violating symmetry scenario. The theoretical model adopted consists of a real massive scalar quantum field confined in a region between two large parallel plates, having its dynamics governed by a modified Klein–Gordon equation that presents a Lorentz symmetry-breaking term. In this context, we admit that the quantum field obeys specific boundary conditions on the plates. The Lorentz-violating symmetry is implemented by the presence of an arbitrary constant space-like vector in a CPT-even aether-like approach, considering a direct coupling between this vector with the derivative of the field in higher order. The modification of the Klein–Gordon equation produces important corrections on the Casimir energy and pressure. Thus, we show that these corrections strongly depend on the order of the higher derivative term and the specific direction of the constant vector, as well as the boundary conditions considered.

Multiple Scattering Expansion for Dielectric Media: Casimir Effect.

Recent measurements of Casimir forces have provided evidence of an intricate modification of quantum fluctuations of the electromagnetic field in complex geometries. Here we introduce a multiple scattering description for Casimir interactions between bodies of arbitrary shape and material composition, admitting an expansion as a sequence of inter- and intra-body wave scatterings. Interactions in complex geometries can be computed within the current experimental resolution from typically a few wave scatterings, notably without any apriori knowledge of the scattering amplitudes of the bodies. Some first applications demonstrate the power of the approach.

Effect of Epsilon-Near-Zero Modes on the Casimir Interaction between Ultrathin Films.

Vacuum fluctuation-induced interactions between macroscopic metallic objects result in an attractive force between them, a phenomenon known as the Casimir effect. This force is the result of both plasmonic and photonic modes. For very thin films, field penetration through the films will modify the allowed modes. Here, we theoretically investigate the Casimir interaction between ultrathin films from the perspective of force distribution over real frequencies for the first time. Pronounced repulsive contributions to the force are found due to the highly confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only exist in ultrathin films. These contributions persistently occur around the ENZ frequency of the film irrespective of the interfilm separation. We further associate the ENZ modes with a striking thickness dependence of a proposed figure of merit (FOM) for conductive thin films, suggesting that the motion of objects induced by Casimir interactions is boosted for deeply nanoscale sizes. Our results shed light on the correlation between special electromagnetic modes and the vacuum fluctuation-induced force as well as the resulting mechanical properties of ultrathin ENZ materials, which may create new opportunities for engineering the motion of ultrasmall objects in nanomechanical systems.