Casimir Effect Research Articles

Preparation of squeezed light with low average photon number based on dynamic Casimir effect

It is well known that squeezed states can be produced by nonlinear optical processes, such as parametric amplification and four wave mixing, in which two photons are created or annihilated simultaneously. Since the Hamiltonian of the dynamic Casimir effect contains a 2 and a +2, photons in such a process are also generated or annihilated in pairs. Here we propose to get squeezed light through the dynamic Casimir effect. Specifically, we demonstrate it from the full quantum perspective and the semiclassical perspective successively. Different from previous work, we focus on generating squeezed states with the lowest average photon number, because such squeezed states have better quantum properties. For the full quantum picture, that is, phonons also have quantum properties, when the system is initially in the excited state of phonons, squeezed light cannot be generated during the evolution, but the light field can collapse to the squeezed state by measuring the state of phonons. When the phonon is treated as a classical quantity, that is, the cavity wall is continuously driven, squeezed light with the minimum average photon number will be generated in the case of off-resonance. This will play a positive role in better regulating the photon state generated by the dynamic Casimir system in the future.

Magnetic corrections to the fermionic Casimir effect in Horava-Lifshitz theories

In this paper, I investigate the effect of a magnetic field on the Casimir effect due to a massless and charged fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I focus on the case of a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this investigation using the [Formula: see text]-function technique that allows me to obtain Casimir energy and pressure in the presence of a uniform magnetic field orthogonal to the plates. I investigate the cases of the parameter associated with the violation of Lorentz invariance being even or odd and the cases of weak and strong magnetic field, examining all possible combinations of the above quantities. In all cases I obtain simple and very accurate analytic expressions of the magnetic field-dependent Casimir energy and pressure.

Stopping to reflect: Asymptotic static moving mirrors as quantum analogs of classical radiation

Radiation from an accelerating charge is a basic process that can serve as an intersection between classical and quantum physics. We present two exactly soluble electron trajectories that permit analysis of the radiation emitted, exploring its time evolution and spectrum by analogy with the moving mirror model of the dynamic Casimir effect. These classical solutions are finite energy, rectilinear (nonperiodic), asymptotically zero velocity worldlines with corresponding quantum analog beta Bogolyubov coefficients. One of them has an interesting connection to uniform acceleration and Leonardo da Vinci's water pitcher experiment.

Nonequilibrium Casimir–Polder Interaction between Nanoparticles and Substrates Coated with Gapped Graphene

The out-of-thermal-equilibrium Casimir–Polder force between nanoparticles and dielectric substrates coated with gapped graphene is considered in the framework of the Dirac model using the formalism of the polarization tensor. This is an example of physical phenomena violating the time-reversal symmetry. After presenting the main points of the used formalism, we calculate two contributions to the Casimir–Polder force acting on a nanoparticle on the source side of a fused silica glass substrate coated with gapped graphene, which is either cooler or hotter than the environment. The total nonequilibrium force magnitudes are computed as a function of separation for different values of the energy gap and compared with those from an uncoated plate and with the equilibrium force in the presence of graphene coating. According to our results, the presence of a substrate increases the magnitude of the nonequlibrium force. The force magnitude becomes larger with higher and smaller with lower temperature of the graphene-coated substrate as compared to the equilibrium force at the environmental temperature. It is shown that, with increasing energy gap, the magnitude of the nonequilibrium force becomes smaller, and the graphene coating makes a lesser impact on the force acting on a nanoparticle from the uncoated substrate. Possible applications of the obtained results are discussed.

Yukawa–Casimir wormhole model in F(R,T) framework

There is an unavoidable association of traversability of wormholes to the violation of null energy condition which in turn indicates the presence of exotic or non-exotic matter in the wormhole geometry. The exotic matter possesses the negative energy that is required to sustain the wormhole. Recently studies are done to solve this problem so as to avoid the exotic matter. In this work, we attempt to find such solution in the framework of [Formula: see text] gravity where [Formula: see text], here [Formula: see text] and [Formula: see text] are Ricci scalar and trace of energy momentum tensor respectively, using the Yukawa–Casimir shape function. For Yukawa–Casimir wormhole, it is assumed that the exotic energy is sourced from the Casimir energy density. We have examined the energy conditions using Yukawa–Casimir shape function [Formula: see text] where [Formula: see text] is a positive mass scale. We have taken different values of [Formula: see text] to study the role of Yukawa–Casimir energy in formation of traversable wormholes. The equilibrium aspect of the model is also investigated with the help of TOV equation.

Gravity from thermodynamics: Optimal transport and negative effective dimensions

We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory of optimal transport to the Raychaudhuri equation in the internal space, where the warp factor introduces effective notions of curvature and (negative) internal dimension. When the Reduced Energy Condition is satisfied, concavity can be characterized in terms of the cosmological constant \LambdaΛ; as a consequence, the masses of the spin-two Kaluza-Klein fields obey bounds in terms of \LambdaΛ alone. We show that some Cheeger bounds on the KK spectrum hold even without assuming synthetic Ricci lower bounds, in the large class of infinitesimally Hilbertian metric measure spaces, which includes D-brane and O-plane singularities. As an application, we show how some approximate string theory solutions in the literature achieve scale separation, and we construct a new explicit parametrically scale-separated AdS solution of M-theory supported by Casimir energy.

Casimir effect in 2+1 Hořava gravity

We study the Casimir effect of a membrane embedded in 2+1 dimensions flat cone generated by a massive particle located at the origin of the coordinate system. The flat cone is an exact solution of the nonprojectable Hořava theory, similar to general relativity. We consider a scalar field satisfying Dirichlet boundary conditions, and regularize the spectrum using the ζ–function technique. In addition, we include the effects of temperature in our analysis. Our results show that the Casimir force depends on three factors: the anisotropic scaling z, the mass of the point particle, and the temperature.

Boundary states and non-Abelian Casimir effect in lattice Yang-Mills theory

Boundary states and non-Abelian Casimir effect in lattice Yang-Mills theory

Robust QFT control design for a multivariable torsion/bending of rotational nanoscanner

This paper proposes a reasonable, practical, and novel method for designing a robust controller for two degrees of freedom nano-electromechanical scanners based on the combination of quantitative feedback theory (QFT) and the Taguchi method. Although the main primary of this paper devotes to rotational control, an investigation of two-degree freedom (rotational/bending) is studied by employing the Taguchi method. A moveable main plate suspended by two nano-beams over a fixed substrate electrode is used to represent the scanner. The nanoscanner is thoroughly analyzed using the most comprehensive modeling design, considering the elastic, electrical, Casimir force and moment, and squeezes film damping. The nanoscanner’s governing equations are initially derived by considering both rotation and deformation. In addition, because the size dependency of materials is significant in ultra-small structures, we developed the constitutive equations within the context of the modified couple stress theory to integrate the effect of scale dependency. Next, system uncertainties have been wholly addressed to achieve an accurate model. As a result, using robust control methods such as quantitative feedback theory to precisely control nano-scanners in the presence of uncertainties is inevitable. The quantitative feedback approach transforms the nonlinear plant into a family of linear uncertain plants in the first part. This is accomplished using a fixed-point theorem, after which appropriate disturbance rejection boundaries are discovered. In this problem, quantitative feedback controllers and checking the system’s stability at any frequency and time are intended to solve the tracking problem and the disturbance rejection issue. Due to the uncertainty associated with the system model’s complexity and accuracy, we employ a QFT controller to control the system. Moreover, because this system has only one input and two outputs, and changing the controller’s gain is complicated, the Taguchi method has been employed to enhance better performance. Nonlinear simulations of the tracking issue are carried out, and the results demonstrate the effectiveness of the developed controllers and prefilters. The findings show that using the suggested approach effectively overcomes the challenges to robust control of a nonlinear rotational nanoscanner, and also the system achieves the best angle and deflection adjustment accuracy.

The universality of black hole thermodynamics

The thermodynamic properties of black holes — temperature, entropy and radiation rates — are usually associated with the presence of a horizon. We argue that any extremely compact object (ECO) must have the same thermodynamic properties. Quantum fields just outside the surface of an ECO have a large negative Casimir energy similar to the Boulware vacuum of black holes. If the thermal radiation emanating from the ECO does not fill the near-surface region at the local Unruh temperature, then we find that no solution of gravity equations is possible. In string theory, black holes microstates are horizonless quantum objects called fuzzballs that are expected to have a surface [Formula: see text] outside [Formula: see text]; thus the information puzzle is resolved while preserving the semiclassical thermodynamics of black holes.

Larmor Temperature, Casimir Dynamics, and Planck’s Law

Classical radiation from a single relativistically accelerating electron is investigated where the temperature characterizing the system highlights the dependence on acceleration. In the context of the dynamic Casimir effect with Planck-distributed photons and thermal black hole evaporation, we demonstrate analytic consistency between the ideas of constant acceleration and equilibrium thermal radiation. For ultra-relativistic speeds, we demonstrate a long-lasting constant peel acceleration and constant power emission, which is consistent with the idea of balanced equilibrium of Planck-distributed particle radiation.

Sensitivity of actuation dynamics of Casimir oscillators on finite temperature with topological insulator materials: Response of repulsive vs attractive interactions

We explore the sensitivity of repulsive and attractive Casimir interactions on thermal fluctuations in topological insulator materials, and the associated effects on non-linear actuation towards chaotic motion. For system at low temperature and applied magnetization in the same direction, by increasing the temperature the sensitivity of the Casimir force to the magnetization, at large separations, weakens. Moreover, by increasing the temperature the repulsive force vanishes for weak magnetization. Furthermore, for conservative systems the stable actuation area for high temperature does not show strong sensitivity to changes of the magnetization and the magnetoelectric effect. For non-conservative system with weak magnetization in the same direction leading to attractive Casimir forces, increment of the temperature increases the possibility for occurrence of chaotic motion.

Zero Casimir force in axion electrodynamics and the search for a new force

Zero Casimir force in axion electrodynamics and the search for a new force

Modeling and nonlinear dynamic analysis of angular velocity system of 2-DOF aerial manipulator

This paper establishes the dynamic model of the angular velocity system of the 2-DOF (degree of freedom) aerial manipulator, describes the coupling relationship between the quadrotor aircraft and the manipulator, and provides the rotational speed relationship of each propeller during open-loop control. On this basis, the dynamic parameters, the nonlinear dynamics under static and dynamic conditions, and the Casimir energy of the system are studied in four parts. In the part of system dynamics parameters, the influence of manipulator configurations and postures on system moment of inertia, yaw motion, and lifting motion are analyzed, and their influence on gyroscopic effect is discussed. In the nonlinear dynamics of the system under static conditions, this paper analyzes the nonlinear dynamics of a typical aerial manipulator by the nonlinear dynamics methods. It reveals for the first time that the angular velocity of the system can produce dynamic behaviors such as sinks, chaotic oscillations, and period-doubling oscillations. The system is a non-autonomous system when it is under dynamic conditions. In this part, this paper considers the dynamic behaviors of the aerial manipulator in three situations: grasping operation, presence of external interference, and presence of time-varying yaw control quantity. It can be seen from the analysis that the dynamic conditions make the nonlinear dynamic behaviors of the system more complicated, which is worthy of further study. In the energy analysis, the Casimir energy of the three cases in this paper is calculated respectively when the sink, chaotic oscillation, and periodic oscillation are generated, and their mean, variance, and standard deviation are calculated. When the system is a sink, the three indexes are the smallest, the energy consumption is the least, and it is easier to control.

Effective binding potential from Casimir interactions: the case of the Bose gas

We consider the thermal Casimir effect in ideal Bose gases, where the dispersion relation involves both terms quadratic and quartic in momentum. We demonstrate that if macroscopic objects are immersed in such a fluid in spatial dimensionality and at the critical temperature , the Casimir force acting between them is characterized by a sign which depends on the separation D between the bodies and changes from attractive at large distances to repulsive at smaller separations. In consequence, an effective potential which binds the two objects at a finite separation arises. We demonstrate that for odd integer dimensionality , the Casimir energy is a polynomial of degree in D −2. We point out a very special role of dimensionality d = 3, where we derive a strikingly simple form of the Casimir energy as a function of D at Bose–Einstein condensation. We discuss crossover between monotonous and oscillatory decay of the Casimir interaction above the condensation temperature.

Casimir energy and modularity in higher-dimensional conformal field theories

An important problem in Quantum Field Theory (QFT) is to understand the structures of observables on spacetime manifolds of nontrivial topology. Such observables arise naturally when studying physical systems at finite temperature and/or finite volume and encode subtle properties of the underlying microscopic theory that are often obscure on the flat spacetime. Locality of the QFT implies that these observables can be constructed from more basic building blocks by cutting-and-gluing along a spatial slice, where a crucial ingredient is the Hilbert space on the spatial manifold. In Conformal Field Theory (CFT), thanks to the operator-state correspondence, we have a non-perturbative understanding of the Hilbert space on a spatial sphere. However it remains a challenge to consider more general spatial manifolds. Here we study CFTs in spacetime dimensions d > 2 on the spatial manifold T2 × ℝd−3 which is one of the simplest manifolds beyond the spherical topology. We focus on the ground state in this Hilbert space and analyze universal properties of the ground state energy, also commonly known as the Casimir energy, which is a nontrivial function of the complex structure moduli τ of the torus. The Casimir energy is subject to constraints from modular invariance on the torus which we spell out using PSL(2, ℤ) spectral theory. Moreover we derive a simple universal formula for the Casimir energy in the thin torus limit using the effective field theory (EFT) from Kaluza-Klein reduction of the CFT, with exponentially small corrections from worldline instantons. We illustrate our formula with explicit examples from well-known CFTs including the critical O(N) model in d = 3 and holographic CFTs in d ≥ 3.

Casimir–Polder Force on Atoms or Nanoparticles from Gapped and Doped Graphene: Asymptotic Behavior at Large Separations

The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found based on the first principles of thermal quantum field theory, are used. It is shown that for graphene the separation distances, starting from which the zero-frequency term of the Lifshitz formula contributes more than 99% of the total Casimir–Polder force, are less than the standard thermal length. According to our results, however, the classical limit for graphene, where the force becomes independent of the Planck constant, may be reached at much larger separations than the limit of the large separations determined by the zero-frequency term of the Lifshitz formula, depending on the values of the energy gap and chemical potential. The analytic asymptotic expressions for the zero-frequency term of the Lifshitz formula at large separations are derived. These asymptotic expressions agree up to 1% with the results of numerical computations starting from some separation distances that increase with increasing energy gaps and decrease with increasing chemical potentials. The possible applications of the obtained results are discussed.

The Casimir effect in a dilute Bose gas in broken symmetry phase within the improve Hartree–Fock approximation

The Casimir effect in a weakly interacting Bose gas confined between two parallel plates is studied at finite temperature, which is smaller than the phase transition temperature, within improved Hartree–Fock (IHF) approximation, in which the number of the Goldstone bosons are conserved. When condensate and non-condensate phases co-exist, considering the contribution of the two-loop diagrams, the order-parameter and effective mass are not constant. The Casimir energy and resulting Casimir force are separated into two parts: the one corresponds to the corresponding one-loop approximation, and the other is associated with the contribution of the two-loop diagrams. Our result can be reduced to the one for weakly interacting gas at zero temperature, or for the ideal Bose gas.

Quale mechanics as a metaphysical weltanschauung of quantum mechanics

The term Quale Mechanics is proposed here as describing the qualitative aspects of Quantum Mechanics that are susceptible of metaphysical considerations. The aim of Quale Mechanics is to distill the quantum discourse to its pillars in order to construct its proper – philosophical in nature – quale discourse. The framework of the discussion is initiated by revisiting the platonic approach of the manner in which knowledge is perceived/processed, and then by discussing the four sapiential stages before arriving at concept of the eide. The sensible-suprasensible dichotomy is exposed by contrasting aistheta to the eide. A discussion on the historical development and the foundation of the pillars of Quantum Mechanics is followed. This includes Planck’s solution for the black-body radiation problem with the introduction of quanta – in conflict with Newtonian physics – followed by Einstein’s explanation of the photoelectric effect and the implications involving the dual nature of light (particle vs. wave) and two generalizations of the quantum character of matter: the planetary model of the atom by Bohr, and the dual particle-wave character of electron demonstrated by de Broglie. The subsequent distillation of these semi-classical concepts into more abstract mathematical concepts by Heisenberg, Born, Dirac and Pauli are then reviewed – with Heisenberg’s uncertainty principle and with the concept of wavefunction as landmarks that unmistakably departs from the classical deterministic view of matter. A representative illustration of these achievements is given by the Casimir effect – with implications for gravity and an illustration of how vacuum can in fact not be considered to be truly void. Quantum Mechanics, as the most accurate mathematical framework which can be employed in order to describe and predict the natural phenomena occurring at the atom-size dimensions of reality, may thus be considered as the root from which the concept of Quale Mechanics is emerged in order to construct the parallel between the metaphysical existence and the quantum physical wavefunction collapse. It is concluded that, within its underlying, Quantum Mechanics is a (hopefully fruitful) reiteration of the Ancient Greek Weltanschauung.

The Casimir interaction in a nonlocal electrolyte slab

In this paper, the Casimir force per unit area across a nonlocal slab of an electrolyte between two semispaces of ordinary materials has been studied through the scattering approach. Because of the insufficiency of Maxwell’s boundary conditions, additional boundary conditions are used as well. The numerical calculations show that for polystyrene semispaces at small separations, ascending the concentration causes intensifying the Casimir pressure. However, it is illustrated that in the case of silver substrates the Casimir pressure has the same amount for two electrolyte concentrations and this intensification does not occur by increasing the concentration. At small separations for polystyrene semispaces, the Hamaker coefficient has two different magnitudes corresponding to 90 and 0.9[Formula: see text]mM concentrations, but for silver substrates the Hamaker coefficient starts from the same value for both concentrations.