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...
It is known that the fundamental Lifshitz theory, which is based on the first principles of thermal quantum field theory, experiences difficulties when compared with precise measurements of the Casimir force. We analyzed the nonconventional fit of th...
The present study deals with the nonlinear forced vibration of an axially functionally graded beam subjected to an electromagnetic actuator, moving load, and Casimir force, considering the curvature of the beam and it resting on a nonlinear elastic W...
We investigate the finite-temperature Casimir interaction between two delta-function potentials in a
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 thermodynam...
Considering a representation space for a group of unimodular
This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown...
We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder for...
The explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geome...
Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We i...
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 stati...
We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting from the first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this formalism, the...
We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived...
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...
We present an analytic continuation of the central charge c in two-dimensional conformal field theory (2D CFT), modeled as a Nevanlinna function—an analytic map from the upper half-plane to itself. Motivated by the structure of vacuum energies...
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 tre...
Wormholes require negative energy, and therefore an exotic matter source. Since Casimir’s energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently a full solution for
This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates wit...
We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the...
A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characte...
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He
We develop a Green’s functions scattering method for systems with Chern–Simons plane boundary layers on dielectric half-spaces. The Casimir pressure is derived by evaluation of the stress tensor in a vacuum slit between two half-spaces. T...
We investigate the quantum forces occurring between the defects and/or boundaries of a conformal field theory (CFT). We propose to model imperfect defects and boundaries as localized relevant double-trace operators that deform the CFT. Our focus is o...
We consider the Casimir pressure between two graphene sheets and contributions to it determined by evanescent and propagating waves with different polarizations. For this purpose, the derivation of the 2-dimensional (2D) Fresnel reflection coefficien...
The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico a...
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 b...
We revisit the problem of the Casimir force between high-Tc superconductors below and above the critical temperature for the superconducting transition. Ceramic superconductors exhibit a different temperature dependence of the reflectivity when switc...
We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional
It is well known that the Casimir force calculated at large separations using the Lifshitz theory differs by a factor of 2 for metals described by the Drude or plasma models. We argue that this difference is entirely determined by the contribution of...
The mean-field model (MFM) is the workhorse of statistical mechanics: one normally accepts that it yields results which, despite differing numerically from correct ones, are not “very wrong”, in that they resemble the actual behavior of t...
In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au...
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 ph...
Lie-algebraic Poisson structures, related to the superalgebra of super-pseudodifferential operators on the circle over the even component of the
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 n...
The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electrom...
Herein we demonstrate the dramatic effect of non-locality on the plasmons which contribute to the Casimir forces, with a graphene sandwich as a case study. The simplicity of this system allowed us to trace each contribution independently, as we obser...
We consider the Casimir interaction energy between a plane and a sphere of radius R at finite temperature T as a function of the distance of closest approach L. Typical experimental conditions are such that the thermal wavelength
Poisson structures related to affine Courant-type algebroids are analyzed, including those related with cotangent bundles on Lie-group manifolds. Special attention is paid to Courant-type algebroids and their related R structures generated by suitabl...
In this study, we perform a theoretical study of light propagation properties in two-dimensional square photonic crystals (PCs) following Bravais–Moiré (BM) patterns composed of copper oxide high-temperature superconductors (HTSCs). The...
We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the
It is known 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 spee...
This paper investigates the dynamic behavior of a Kolmogorov-type permanent-magnet synchronous generator for wind power systems. Firstly, the chaotic model of the salient-pole permanent-magnet synchronous generator is derived and subsequently transfo...
We derive the quantum analogues of some recently discovered symmetry relations for time correlation functions in systems subject to a constant magnetic field. The symmetry relations deal with the effect of time reversal and do not require—as in the f...
In this work, a closed isotropic universe with scalar and spinor fields is considered within the framework of the extended phase space approach. Unlike conventional canonical quantization that yields the Wheeler–DeWitt equation, our method allows us...
After the first clear evidence of the recession—at very high speeds—of the spiral nebulae was announced by V.M. Slipher in 1914, as a result of his work started in 1912, it still took several decades to properly understand the phenomenon...
Micro functionally graded material (FGM) structures are able to have proper functions in vast environments. In this paper, nonlinear governing equations of the size-dependent micro-switch are derived using modified couple stress theory. Effective ext...
This Special Issue of Nutrients: Vitamin D and Human Health celebrates diversity in vitamin D research with articles from bench-to-bedside, examining mechanisms, epidemiology, and clinical issues in the management of non-skeletal disease following th...
We study the phase-space dynamics of quantum systems with
We present the theoretical description of a resistive nanoswitch designated for a change-over between the two operation modes by calculating the electric, elastic, dispersion (van der Waals and Casimir), and also exchange repulsive forces in its conf...
While synthetic biology has traditionally focused on creating biological systems often through genetic engineering, emerging technologies, for example, implantable pacemakers with integrated piezo-electric and tribo-electric materials are beginning t...
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