It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

Here we calculate the deflection angle of photon by Casimir wormhole in weak limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on Gaussian optical metric and find deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. After calculating the deflection angle of Casimir wormhole. Now, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

We investigate the influence of the Abrikosov vortex lattice on the Casimir force in a setup constituted by high-temperature superconductors subject to an external magnetic field. The Abrikosov lattice is a property of type II superconductors in which normal and superconducting carriers coexist and these latter define a periodic pattern with squared symmetry. We find that the optical properties determined by spatial redistribution of the superconducting order parameter induce Casimir forces with a periodic structure whose minimal strengths coincide with the vortex cores.

Here, we investigate the actuation dynamics of a micro device with different intervening liquids between the actuating components under the influence of Casimir and dissipative hydrodynamic forces. This is enabled via phase space portraits, which demonstrate that by increasing the dielectric response of the intervening layer the device may not come into stiction due to the decreasing in magnitude Casmir force. Moreover, it is feasible to expand area of motion using intervening liquids with lower dynamic viscosity or increasing the slip length of the intervening fluid. Finally, under the influence of an external driven force, which is the realistic case for possible applications, the system can reach stable oscillation at larger separations with an amplitude higher for the liquid that lead to lower Casimir and hydrodynamic forces.

This research work investigates the possibility of shielding gravity. The ultimate purpose of this work is to understand the reality behind the concept of Gravitational Shielding (GS) and time dilation. Since the 19th century, scientists have tried to arrive at an understanding of GS via the use of various experiments. Unfortunately, some experiments failed to prove the existence of gravitational shielding, whereas some results proclaimed the possibility of attaining GS. The original phenomenon exhibited by nature cannot easily be understood, but some experiments have demonstrated that the answer may lie behind the mysterious GS. If GS is proved, then in the future, it would be possible to travel across black holes by defying gravity or through any bigger mass having high gravitational field. To unravel the mystery of GS, this work investigates the history of GS and considers the future vision of technologically advanced spacecraft or other warp drive mechanisms with appropriate gravitational shielding. Though the problem is very complex, this research work tries to come to a deeper understanding and explanation of the complexity involved in achieving gravitational shielding.

It is familiar that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with $\varepsilon\mu=1$, a so-called isorefractive or diaphanous ball. Here we re-examine that example, and attempt to extend it to an electromagnetic $\delta$-function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.

The Casimir–Lifshitz friction force and the heating rates of two metal plates with a narrow vacuum gap between them during nonrelativistic motion of one of them are calculated analytically and numerically within the framework of fluctuation electrodynamics. Changes in material properties are taken into account using the Bloch-Grüneisen and modified Bloch-Grüneisen (with finite residual resistance) resistivity models within the Drude approximation. It is shown that identical plates with the same initial temperature have the same heating rate, determined by the power of the friction force, and the possibility of measuring the friction force from the heating kinetics of nonmagnetic metal plates with temperatures of 1–10 K is substantiated.

One of the biggest challenges in modern physics is how to unify gravity with quantum theory. There is an absence of a complete quantum theory of gravity, and conventionally it is thought that the effects of quantum gravity occur only at high energies (Planck scale). Here we suggest that certain novel quantum effects of gravity can become significant even at lower energies and could be tested at laboratory scales. We also suggest a few indirect effects of dark energy that can show up at laboratory scales. Using these ideas, we set observational constraints on radio recombination lines of the Rydberg atoms. We further suggest that high-precision measurements of Casimir effects for smaller plate separation could also show some manifestations of the presence of dark energy.

The Casimir effect can either work over very short distances or at very low temperatures. At the cosmic scale, we naturally deal with long distances, but at the same time, we encounter extraordinarily low temperatures, namely the CMB (Cosmic Microwave Background) tem- perature. Recently, there has been increased interest in the Casimir effect and its implications in cosmology. Here, we briefly demonstrate that the luminosity and radiation pressure of the CMB is mathematical identical to a theoretical Casimir effect within the Hubble sphere, or actually our solution seems to be valid for any Schwarzschild black hole. The Casimir effect forevery Schwarzschild black hole is identical. This also include the Hubble sphere if we treat it as a Schwarzschild black hole that is related to increased interest in black hole cosmology.

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.

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the universal formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors. Expressions for the electric and magnetic fields of a photon during its interaction with an electron.Thus, a unified way to describe bosons and fermions in spinor space is proposed. Each spinor using the same formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field, coordinates and momentum vectors of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.While quantum mechanics treats probability as a real number, quantum field theory deals with probability as a four-dimensional real vector. The place of the probability amplitude, which in quantum mechanics is a complex number, in quantum field theory is taken by a complex spinor.In the same way as in quantum mechanics the processes of propagation and interaction are described at the level of complex probability amplitudes, and the final result is translated into a real probability value, so in quantum field theory all processes should be described in terms of complex spinor space, and the result is translated into the form of a real vector in Minkowski space.The presented approach, at its proper development, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

In cosmology dark energy and dark matter are included in the ΛCDM model, but they are still completely unknown. Because in black holes Lorentz invariance seems not to be applicable for curved space-time, we introduce a model for a reduced speed of light in black holes due to quantum gravity effects and the Heisenberg uncertainty relation. Then black holes are a source for a scalar field with dark energy characteristics. This model has no information paradox for black holes because particles / radiation entering the black hole are redshifted in their wavelength that far that the wavelength has the size of the Schwarzschild radius and thus they are in some way "frozen" in the black hole. We show that the scalar field also has characteristics of dark matter shortly after Planck time, when we use a Big Bounce model. This model also presents an alternative to cosmological inflation with the possibility to solve the flatness and horizon problem and the problem of density fluctuations.

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.