Search Results (12)

The method of the adhered cantilever, borrowed from microtechnology, can help in gaining fundamental knowledge about dispersion forces acting at distances of about 10 nm, which are problematic to access in the usual Casimir-type experiments. A recently presented setup measures the shape of cantilevers with high precision, which is needed for analyzing the involved forces. The first measurements reveal several nonidealities crucial for the data analysis. In this paper, a generalized formula is deduced that relates the parameters of a cantilever to the adhesion energy. The application of the formula is demonstrated using the first test result from the setup, where a silicon cantilever adhered to a substrate sputters with ruthenium. Detailed information of the roughness of interacting surfaces, which deviates significantly from the normal distribution, is emphasized. Although not crucial, the electrostatic contribution can be significant due to the slight twisting of the cantilever. The theoretical prediction of the adhesion energy is based on Lifshitz theory. Comparing theory and experiment yields a contact distance of 45 nm and an adhesion energy of 1.3 µJ/m², resulting from the Casimir–Lifshitz forces. Significant uncertainties arise from the uncontrolled electrostatic contribution. Factors that need to be addressed to measure weak adhesion between rough surfaces are highlighted. Full article

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore $f\left(R\right)$ theories and then explore some wormhole solutions in $f\left(R\right)$ theories, including Lovelock gravity and Einstein Dilaton Gauss–Bonnet (EdGB) gravity. For completeness, we have also reviewed ‘Other wormholes’ such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity (NLG) wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required. Full article

In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell. Full article

In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics. Full article

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynamics” then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau’s cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain’s PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain’s works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie–Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation. Full article

In this paper, we consider the motion of an asymmetric heavy gyrostat, when its center of mass lies along one of the principal axes of inertia. We determine the possible permanent rotations and, by means of the Energy-Casimir method, we give sufficient stability conditions. We prove that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space, by the action of two spinning rotors, one of them aligned along the principal axis, where the center of mass lies. We also derive necessary stability conditions that, in some cases, are the same as the sufficient ones. Full article

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula. Full article

We offer in this review a description of the vacuum energy of self-similar systems. We describe two views of setting self-similar structures and point out the main differences. A review of the authors’ work on the subject is presented, where they treat the self-similar system as a many-object problem embedded in a regular smooth manifold. Focused on Dirichlet boundary conditions, we report a systematic way of calculating the Casimir energy of self-similar bodies where the knowledge of the quantum vacuum energy of the single building block element is assumed and in fact already known. A fundamental property that allows us to proceed with our method is the dependence of the energy on a geometrical parameter that makes it possible to establish the scaling property of self-similar systems. Several examples are given. We also describe the situation, shown by other authors, where the embedded space is a fractal space itself, having fractal dimension. A fractal space does not hold properties that are rather common in regular spaces like the tangent space. We refer to other authors who explain how some self-similar configurations “do not have any smooth structures and one cannot define differential operators on them directly”. This gives rise to important differences in the behavior of the vacuum. Full article

With large-scale development of offshore wind power and the increasing scale of power grid interconnection, more and more attention has been drawn to the stable operation of wind power units. When the wide area measurement system (WAMS) is applied to the power system, the time delay mainly occurs in the signal measurement and transmission of the power system. When 10MW wind turbines transmit information through complex communication network, time delay often exists, which leads to the degradation of performance and instability for system. This affects the normal operation of a wind farm. Therefore, in this paper, the distributed control problem of doubly fed wind turbines with input time delay is studied based on the Hamiltonian energy theory. Firstly, the Port-controlled Hamiltonian system with Dissipation (PCH-D) model is implemented with the Hamiltonian energy method. Then, the Casimir function is introduced into the PCH-D model of the single wind turbine system to stabilize the time delay. The wind turbine group is regarded as one network and the distributed control strategy is designed, so that the whole wind turbine cluster can remain stable given a time delay occurring in the range of 30–300 ms. Finally, simulation results show that the output power of the wind turbine cluster with input delay converges to the expected value rapidly and remains stable. Additionally, the system error caused by time delay is greatly reduced. This control method can effectively solve the problem of input time delay and improve the stability of the wind turbine cluster. Moreover, the method proposed in this paper can adopt the conventional time step of dynamic simulation, which is more efficient in calculation. This method has adaptability in transient stability analysis of large-scale power system, however, the third-order mathematical model used in this paper cannot be used to analyze the internal dynamics of the whole power converter. Full article

We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet–Liouvillian by applying the Floquet method and Brillouin–Wigner–Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy-dependent self-energy. The obtained effective Floquet–Liouvillian exhibits the two competing instabilities, i.e., parametric and resonance instabilities, which determine the stationary mode as a result of the balance between them in the dissipative DCE. Solving the complex eigenvalue problem of the Floquet–Liouvillian, we have determined the stationary mode with vanishing values of the imaginary parts of the eigenvalues. We find a new non-local multimode DCE represented by a multimode Bogoliubov transformation of the cavity mode and the photon band. We show the practical advantage for the observation of DCE in that we can largely reduce the pump frequency when the cavity system is embedded in a narrow band photonic crystal with a bandgap. Full article

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point field, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The first two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive. Full article

We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the $SU\left(N\right)$ adjoint representation to other matrix models, namely the free $SO\left(N\right)$ and $Sp\left(N\right)$ adjoint models as well as the free $U\left(N\right)\times U\left(M\right)$ bi-fundamental and $O\left(N\right)\times O\left(M\right)$ bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the Character Integral Representation of the Zeta Function (CIRZ) method, which we recently introduced. We also elaborate on possible ambiguities in the application of this method. Full article