Conducting Parallel Plates Research Articles

Perturbative versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories

We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well-defined (rigorous) mathematical sense, as well as some of the few existent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part, we apply Tao’s method to the Casimir effect in its simplest form, consisting of perfectly conducting parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly proposed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles. Various problems (mostly open) are finally discussed in connection with concrete models.

Graphene H-Waveguide for Terahertz Lasing Applications: Electromagnetic Quasi-Linear Theory

A novel graphene H-waveguide is proposed for active terahertz components. A graphene film illuminated by strong pumping light shorts the parallel conductor plates. The terahertz modes propagating along this film are amplified at certain conditions. A rigorous electromagnetic (EM) quasi-linear method of analytical calculations of and eigenmodes is used in this paper to select these conditions. Among them is the use of bound modes interacting with graphene plasmons at frequencies of negative graphene resistance, minimizing conductor loss associated with parallel plates, and excluding the current-crowding effect from the waveguide design. The limitations of the used theory are considered, and the applications of this waveguide are proposed.

A Capacitive Sweat Rate Sensor for Continuous and Real-Time Monitoring of Sweat Loss.

Individualized measurement of sweat loss under heat stress is important in assessing physical performance and preventing heat-related illness for athletes or individuals working in extreme environments. The objective of this work was to develop a low-cost and easy-to-fabricate wearable sensor that enables accurate real-time measurement of sweat rate. A capacitive-type sensor was fabricated from two conducting parallel plates, plastic insulating layers, and a central microfluidic channel formed by laser cutting a plastic film. The device has no microfabricated electrodes and is assembled using adhesive tape. Sensor accuracy was validated at different flow rates and confirmed using an equivalent circuit model of the device. On-body measurements demonstrate the feasibility of real-time measurements and show good agreement with values determined from a conventional sweat collection device.

Modular invariance in finite temperature Casimir effect

The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

Force on Dielectric by the Fringe Field: Comparison to Dielectrophoretic Force

In this manuscript, the force exerted on the dielectric in the fringe field from the two conducting parallel plates with applied electrical potential was calculated and found to be an effective micro/nanoscale manipulation tool. The conformal mapping was employed to obtain the fringe field generated from the edges of the plates. The strong gradient of the fringe field near the edges was manifested in both parametric mapping and simulation. It was found that the force analytically obtained from the fringe field was proportional and directed to the gradient of the squared electric field. The result was compared to dielectrophoresis (DEP).

Review on Laminated Busbars used in High Frequency Inverters

Improvement in the efficiency and cost in the high frequency inverter will play a major role in its applications like electrical vehicles (EV). A high voltage IGBTs are used in inverters to bear the voltage peaks across the IGBT switch at the turning off period of switch. By decreasing the value of voltage peak, can reduce the voltage rating of IGBT switch, by which the system cost will decrease. Decreasing the value of voltage peak can be achieved by decreasing the inductance of the inverter circuit which includes turned on switch inductance, DC link capacitors inductance and connecting wires inductance. By replacing the connecting wires with a laminated busbar in an inverter, the inductance value of a connecting wires can be reduced. Laminated bus bar is a parallel conductor plates separated by a dielectric medium. Upper plate is considered as positive plate and lower plate is a negative plate. In this paper it gives a detailed information about laminated busbar with different designs, using different conductive materials, their calculated inductance in ANSYS 3D FEM software and concluding with suitable laminated busbar for high frequency inverter.

NLO radiative correction to the Casimir energy in Lorentz-violating scalar field theory

Violation of the Lorentz symmetry has important effects on physical quantities including field propagators. Therefore, in addition to the leading order, the sub-leading order of quantities may be modified. In this paper, we calculate the next to leading (NLO) radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for ϕ4 theory with a Lorentz-breaking extension. We do the renormalization and investigate these NLO corrections for three distinct directions of the Lorentz violation; temporal direction, parallel and perpendicular to the plates.

Understanding zero-point energy in the context of classical electromagnetism

Today’s textbooks of electromagnetism give the particular solution to Maxwell’s equations involving the integral over the charge and current sources at retarded times. However, the texts fail to emphasise that the choice of the incoming-wave boundary conditions corresponding to solutions of the homogeneous Maxwell equations must be made based upon experiment. Here we discuss the role of these incoming-wave boundary conditions for an experimenter with a hypothetical charged harmonic oscillator as his equipment. We describe the observations of the experimenter when located near a radio station or immersed in thermal radiation at temperature T. The classical physicists at the end of the 19th century chose the incoming-wave boundary conditions for the homogeneous Maxwell equations based upon the experimental observations of Lummer and Pringsheim which measured only the thermal radiation which exceeded the random radiation surrounding their measuring equipment; the physicists concluded that they could take the homogeneous solutions to vanish at zero temperature. Today at the beginning of the 21st century, classical physicists must choose the incoming-wave boundary conditions for the homogeneous Maxell equations to correspond to the full radiation spectrum revealed by the recent Casimir force measurements which detect all the radiation surrounding conducting parallel plates, including the radiation absorbed and emitted by the plates themselves. The random classical radiation spectrum revealed by the Casimir force measurements includes electromagnetic zero-point radiation, which is missing from the spectrum measured by Lummer and Pringsheim, and which cannot be eliminated by going to zero temperature. This zero-point radiation will lead to zero-point energy for all systems which have electromagnetic interactions. Thus the choice of the incoming-wave boundary conditions on the homogeneous Maxwell equations is intimately related to the ideas of zero-point energy and non-radiating ground states which are introduced in classes of modern physics.

Electromagnetic thermal corrections to Casimir energy

In [B. Nazari, Mod. Phys. Lett. A 31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.

One-loop radiative corrections to the QED Casimir energy

In this paper, we investigate one-loop radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for QED theory within the renormalized perturbation theory. In fact, there are three contributions for radiative corrections to the Casimir energy, up to order $\alpha$. Only the two-loop diagram, which is of order $\alpha$, has been computed by Bordag et. al (1985), approximately. Here, up to this order, we consider corrections due to two one-loop terms, i.e., photonic and fermionic loop corrections resulting from renormalized QED Lagrangian, more precisely. Our results show that only the fermionic loop has a very minor correction and the correction of photonic loop vanishes.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to the situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked agains numerical simulations with the CSRZ computer code.

Thermal corrections to the Casimir energy in a general weak gravitational field

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.

Casimir effect of two conducting parallel plates in a general weak gravitational field

We calculate the finite vacuum energy density of the scalar and electromagnetic fields inside a Casimir apparatus made up of two conducting parallel plates in a general weak gravitational field. The metric of the weak gravitational field has a small deviation from flat spacetime inside the apparatus and we find it by expanding the metric in terms of small parameters of the weak background. We show that the found metric can be transformed via a gauge transformation to the Fermi metric. We solve the Klein-Gordon equation exactly and find mode frequencies in Fermi spacetime. Using the fact that the electromagnetic field can be represented by two scalar fields in the Fermi spacetime, we find general formulas for the energy density and mode frequencies of the electromagnetic field. Some well-known weak backgrounds are examined and consistency of the results with the literature is shown.

Electrocapillary drop actuation and fingering instability in a planar Hele-Shaw cell

The electrically driven displacement of a viscous poorly conducting Newtonian fluid drop positioned between conducting parallel plates is studied both theoretically and experimentally. A mathematical expression for the average-steady velocity is developed by using Darcy flow analysis with an interface pressure that includes a contribution from Maxwell stresses at the advancing gas-liquid boundary. Experiments were performed using silicone oil at plate separation distances less than the capillary length for voltages ranging 250-750 V resulting in a change in velocity of approximately one order of magnitude. This suggested that the driving force was proportional to the square of the applied voltage, a feature that is common among fluid motion driven by electrical phenomena. The trailing interface revealed a disturbance for large fluid displacements that is analogous to a fingering instability. The channel widths were small such that we could predict the transition from a single finger that grows linearly to a single finger that grows exponentially and to multiple fingers that grow exponentially, all occurring within the range of voltages studied. The theory and experiments show good agreement with classic interfacial linear stability analysis.

Finite temperature Casimir effect for massive scalars in a magnetic field

The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.

Steady Flow of Two Conducting Incompressible and Immiscible Fluids Between Two Conducting Plates under Closed Circuit Conditions

This paper discusses the flow of two conducting, viscous, incompressible and immiscible fluids between two conducting parallel plates in presence of an applied transverse magnetic field under general electrical loading conditions. It has been shown that the flow fluxes of the two fluids, the interface velocity and the skin friction on the two plates with the increase of the total current.

FINITE TEMPERATURE CASIMIR EFFECT FOR PERFECTLY CONDUCTING PARALLEL PLATES IN (D + 1)-DIMENSIONAL SPACETIME

We study the finite temperature Casimir effect between perfectly conducting parallel plates in (D + 1)-dimensional spacetime by using zeta-function regularization technique. We get the analytical results for Casimir energy, Casimir free energy, Casimir entropy and Casimir pressure expressed by Riemann zeta function and Bessel function and give the asymptotic expressions for low and high temperature limits. In the case of D = 3, through mathematic transformation, we reproduce the standard results in the literature which is in most times obtained by using Green's function regularization technique.

On the corrections to the Casimir effect depending on the resolution of measurement

The Casimir force $\cF = -\frac{\pi^2\hbar c}{240a^4}$, which attracts to each other two perfectly conducting parallel plates separated by the distance $a$ in vacuum, is one of the blueprints of the reality of vacuum fluctuations. Following the recent conjecture, that quantum fields should be described in terms of the fields depending on the resolution of measurement, rather than the position alone (M.V.Altaisky, Phys. Rev. D 81(2010)125003), we derive the correction to the Casimir energy depending on the ratio of the plate displacement amplitude to the distance between plates.

Quantum Statistical Properties of the Interactions of Atom-Field Entanglement between Conducting Plates

The electromagnetic field inside perfectly conducting parallel plates interacting with two-level atom is investigated. The cavity modes are firstly quantized, allowing the effective Hamiltonian to be evaluated for an electric dipole located at an arbitrary point. Some statistical aspect of this effective Hamiltonian such as the temporal evolution of the atomic inversion and the von Neuman entropy are presented. Theses aspects are sensitive to the changes of the distance between the two plates, which control the number of the propagating of the cavity modes.

Casimir force in the presence of a medium

We investigate the Casimir effect in the presence of a medium by quantizing the electromagnetic field in the presence of a magnetodielectric medium using the path-integral technique. For a given medium with definite electric and magnetic susceptibilities, explicit expressions for the Casimir force are obtained. The Lifshitz formula is recovered and in the absence of a medium the results tend to the original Casimir force between two conducting parallel plates immersed in the quantum electromagnetic vacuum.