Casimir Effect Research Articles

The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities

We consider the two planes at zero temperature with isotropic conductivity that are in relative lateral motion with velocity v and interplane distance a. Two models of conductivity are taken into account—the constant and frequency-dependent Drude models. The normal (perpendicular to planes) Casimir force is analyzed in detail for two systems—(i) two planes with identical conductivity and (ii) one plane that is a perfect metal. The velocity correction to the Casimir energy, ΔvE∝v2, for small enough velocities is used for all considered cases. In the case of constant conductivity, η, the energy correction is ΔvE∝η/a3v/η2 for v≪η≪1.

Casimir effect of a rough membrane in 2 + 1 Hořava–Lifshitz theory

We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz theory in 2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2+1$$\\end{document} dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document}-function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.

Scale limited fields and the Casimir effect

Scale limited fields and the Casimir effect

Thermodynamic entropy production in the dynamical Casimir effect

Thermodynamic entropy production in the dynamical Casimir effect

Examples of atoms absorbing photon via Schrödinger equation and vacuum fluctuations

The absorption of photons by atoms encompasses fundamental quantum mechanical aspects, particularly the emergence of randomness to account for the inherent unpredictability in absorption outcomes. We demonstrate that vacuum fluctuations can be the origin of this randomness. An illustrative example of this is the absorption of a single photon by two symmetrically arranged atoms. In the absence of a mechanism to introduce randomness, the Schrödinger equation alone can govern the time evolution of the process initially. Then, it becomes stuck, and an entangled state of the two atoms emerges. This entangled state consists of two components: in one, the first atom is excited by the photon while the second is in the ground state, and in the other, the second atom is excited while the first remains in the ground state. These components form a superposition state characterized by an unbreakable symmetry in the absence of external influences. Consequently, the absorption process remains incomplete. When vacuum fluctuations come into play, they can induce fluctuations in the weights of these components, akin to Brownian motion. Over time, one component diminishes, thereby breaking the entanglement between the two atoms and allowing the photon absorption process to conclude. The remaining component shows which atom completes the photon absorption. Vacuum fluctuations not only introduce randomness but also have the potential to give rise to the Born rule in this context. Furthermore, the Casimir effect, which is closely tied to vacuum fluctuations, presents a promising experimental avenue for validating this mechanism. Similar studies can also be conducted with varying numbers of atoms.

Intermolecular forces and surface stress residual effects on the size-dependent performance analysis of nanocrystalline micro/nano gyroscopes

This work investigates an electrostatically-actuated vibrating beam micro/nano-gyroscope made of nanocrystalline silicon material. The comprehensive size-dependent micro/nanogyroscope model is developed by couple stress and surface elasticity theories. Then, considering the effects of intermolecular forces (Casimir force and van der Waals force) and surface stress residual, an in-depth investigation was conducted on the performance of the micro/nanogyroscope. The calculation results display that the maximum static deflection, pull-in voltage and natural frequency change obviously with the increase of surface stress residual as the scale varies from micrometer to nanoscale. However, the effect of intermolecular forces on the performance of gyroscopes is exactly the opposite, which improves the prediction of system structural softening deformation phenomenon. Considering the influence of the Casimir and van der Waals forces in micro/nano gyroscopic system will help gyroscopes to obtain reliability and functionality sensitivity, increase the accuracy of predicting static deformation, natural frequency and differential frequency. Moreover, a frequency-domain method using the difference between the two vibration natural frequencies is studied, with changing the scale of the gyroscope under the effect of the intermolecular forces. The numerical simulations exhibit that when considering smaller structure sizes of the gyroscope, strong coupling occurs between the intermolecular forces and surface stress residual, which is helpful for the design of micro/nano gyroscopes.

Search for environment-dependent dilatons

The environment-dependent dilaton field is a well-motivated candidate for dark energy and naturally arises in the strong coupling limit of string theory. In this article, we present the very first experimental constraints on the parameters of this model. For this, we employ data obtained from the qBounce collaboration and the Lunar Laser Ranging (LLR) experiment. Furthermore, we forecast expected constraints for the Casimir And Non Newtonian force EXperiment (Cannex) soon to be realized in an improved setup. Finally, we provide a detailed analysis of the screening mechanism and additional symmetries of the dilaton field theory.

Dynamic and instability analysis of single walled carbon nanotubes with geometrical imperfections resting on elastic medium in a magneto-thermally-electrostatic environment with impact of Casimir force using homotropy perturbation method

The discovery of carbon nanotubes (CNTs) has renewed a major chapter in the field of physics, chemistry, mechanics and materials science owing to their high-quality possession of: excellent tensile strength, high conductivity, high aspect ratio, thermally stable and high chemical stability. In this work, dynamic and instability analysis of single walled carbon nanotube with geometrical imperfection resting on elastic medium in a magneto-thermally-electrostatic environments with impact of Casimir force. However, Eringen nonlocal theory and Hamilton principles are used to develop the nonlinear governing partial differential equations of motions and the governing equations of motion is converted into a duffing equation using Galerkin decomposition method and subsequently, the duffing equation is solve using Homotropic Perturbation Method (HPM), where dynamic responses are obtained. The results obtain depicted that, the effects of magnetic term, thermal term and Pasternak type foundation on dimensionless amplitude-frequency ratio for fixed-fixed and fixed-simple supports make the investigation novelty as it can be used as reference in future study. Finally, the deflection curves show how the compression zone is augmented using Casimir and electrostatic forces and the results obtained shows reasonable accurate.

On a Heuristic Point of View about the Generalization of Curie Law to Cosmic Higgs Fields with the Casimir Effect

On a Heuristic Point of View about the Generalization of Curie Law to Cosmic Higgs Fields with the Casimir Effect

The Casimir Effect in Detail

The Casimir Effect in Detail

DYNAMIC ANALYSIS OF THE VISCOELASTIC MICROTWEEZER UNDER ELECTROSTATIC FORCES AND THERMAL FIELDS

This is the first study to examine the nonlinear dynamic behavior of a microtweezer under electrostatic forces by taking into account viscoelastic effects and linear and nonlinear thermal stresses. The van der Waals (vdW) forces and Casimir intermolecular forces have been included in order to consider more realistic assumptions. Hamilton's principle is applied to derive the nonlinear equations governing the system. A nonlinear partial differential equation has been converted into an ordinary nonlinear differential equation using the Galerkin method. The equations are numerically solved and the results are analyzed at different values of the effective parameters, such as the coefficients of the Casimir force and the vdW forces. Results indicate that the increase in the small size parameter and Casimir and vdW forces results in a decrease in the equivalent stiffness and, therefore, a decrease in the pole's voltage. In addition, the viscoelastic behavior causes a significant change in the stability behavior of the microbeams, and with an increase in damping, the resonance frequency increases by about 33%. Therefore, it is essential to take into account the effect of viscous damping when designing a microtweezer.

Tangential Casimir force in the misaligned system: Magnetic media, real conductors, and a torque

Uncharged parallel plates in the misaligned system can experience a tangential Casimir force between them. We consider the role of magnetic response in this effect by extending the tangential force to magnetic media, and the extension is realized by working out the total zero-point energy of multilayered magnetodielectrics. Then we investigate the tangential force for real conductors by taking into account the temperature dependence of their dielectric constants, and obtain needed results for experimental investigations that are expected to be conducted at room temperature. Thereafter, we discuss a Casimir torque between parallel plates made of isotropic media, which offers a simple way to realize torques for uncharged surfaces.

Large Casimir Flipping Torque in Quantum Trap.

Casimir torque between parallel plates, a macroscopic quantum electrodynamics effect, is known to be induced by dielectric anisotropy and related to the rotational degree of freedom. We here reveal a different type of Casimir torque generated on a Au plate suspended in a quantum trap without recourse to materials anisotropy. As the Au plate deflects from the equilibrium plane with a nonzero flipping angle, the regions departing from and approaching the Teflon-coated Au substrate are subjected to attractive and repulsive Casimir forces, respectively, resulting in a restoring torque about the axis of flipping. For a quantum trap with an equilibrium separation of ∼10 nm, the stiffness per unit area of the Casimir flipping torque can be an order of magnitude larger than those of previously reported dielectric anisotropy-induced rotational torques at the same separation. The large Casimir flipping torque provides the possibility of designing a mechanical oscillator completely dominated by quantum and thermal fluctuations.

Accelerated electron thermometer: observation of 1D Planck radiation

Abstract We report on the observation of thermal photons from an accelerated electron via examination of radiative beta decay of free neutrons measured by the RDK II collaboration. The emitted photon spectrum is shown to corroborate a thermal distribution consistent with the dynamical Casimir effect. Supported by a robust chi-squared statistic, we find the photons reside in a 1D Planck spectrum with a temperature predicted by the moving mirror model. Subject Indices: B50 (Electromagnetic processes and properties), D29 (Nuclear decays and radioactivities (including fission)), and E76 (Quantum field theory on curved space)

Multiplicative anomaly matches Casimir energy for GJMS operators on spheres

An explicit formula to compute the multiplicative anomaly or defect of ζ-regularized products of linear factors is derived, by using a Feynman parametrization, generalizing Shintani-Mizuno formulas. Firstly, this is applied on n-spheres, reproducing known results in the literature. Then, this framework is applied to a closed Einstein universe at finite temperature, namely Sβ1×Sn−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\beta}^1\ imes {S}^{n-1} $$\\end{document}. In doing so, it is shown that the standard Casimir energy (as computed via ζ regularization) for GJMS operators coincides with the accumulated multiplicative anomaly for the shifted Laplacians that build them up. This equivalence between Casimir energy and multiplicative anomaly within ζ regularization, unnoticed so far to our knowledge, brings about a new turn regarding the physical significance of the multiplicative anomaly, putting both now on equal footing. An emergent improved Casimir energy, that incorporates the multiplicative anomaly among the building Laplacians, is also discussed.

Laser-induced heating for the experimental study of critical Casimir forces with optical trapping

Critical Casimir interactions represent a perfect example of bath-induced forces at mesoscales. These forces may have a relevant role in the living systems as well as a role in the design of nanomachines fueled by environmental fluctuations. Since the thermal fluctuations are enhanced in the vicinity of a demixing point of a second-order phase transition, we can modulate the magnitude and range of these Casimir-like forces by slight changes in the temperature. Here, we consider two optical trapped colloidal beads inside a binary mixture. The Casimir interaction is controlled by warming the mixture by laser-induced heating, whose local application ensures high reproducibility. Once this two-particle system is warmed, the critical behavior of different observables allows the system to become its self-thermometer. We use this experimental scheme for analyzing the energetics of a critical colloidal system under a non-equilibrium-driven protocol. We quantify how the injected work can be dissipated to the environment as heat or stored as free energy. Indeed, our system allows us to use the fluctuation theorems framework for analyzing the performance of this critically driven toy model. Our work paves the way for future experimental studies on the non-equilibrium features of bath-induced forces and the design of critically driven nanosystems.

A coherent state approach to the Casimir effect for a massive scalar field in a noncommutative spacetime

In this paper we investigate the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance L, for a massive scalar field in a noncommutative spacetime within a coherent state approach. Noncommutative geometry is implemented by means of modified commutation relations for the spacetime coordinates, thus introducing a fundamental length scale l in the theory. Following a coordinate coherent states approach, we define mean values over the noncommutative spacetime and introduce the massive scalar field theory. We derive an expression for the zero-point energy which we evaluate by means of a dimensional regularization process. We express the Casimir energy in terms of powers of the ratios (l/L)2n in the massless case and (ml2/L)2n in the massive case. Our results are discussed both, theoretically and numerically. We finally estimate boundary effects by introducing an specific model for the plates.

Electrical and thermal control of Fabry-Pérot cavities mediated by Casimir forces

Electrical and thermal control of Fabry-Pérot cavities mediated by Casimir forces

Vacuum Interaction of Topological Strings at Short Distances

The paper provides an extended overview of recent results obtained by the authors in the process of studying the vacuum interaction of topological cosmic strings at short distances, taking into account their transverse size a and the mass m of the quantized field. We consider the case of a massive real-valued scalar field with minimal coupling. It is shown that at the interstring distances significantly larger than the Compton length, lc=1/m, the Casimir effect is damped exponentially. On the other hand, at distances smaller than lc but much larger than the typical string width, the field-mass influence becomes insignificant. In this case, the partial contribution of a massive field to the Casimir energy is of the same order as the contribution of a massless one. At these distances, the string’s transverse size is insignificant also. However, at the interstring distances of the same order as a string radius, the energy of the vacuum interaction of thick strings may significantly surpass the one for two infinitely thin strings with the same mass per unit length.

Holographic thermal observables and M2-branes

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 holographic SCFTs arising on the worldvolume of N M2-branes. We obtain results for the thermal free energy density on S1 × ℝ2, the Casimir energy on T2 × ℝ, and the three leading coefficients in the large temperature limit of the free energy on S1 × S2 valid to subleading order in the large N limit. As a byproduct of our holographic analysis we also present a conjecture for the structure of the large temperature expansion of the thermal free energy of general 3d CFTs on S1 × S2.