A critical discussion of different methods and models in Casimir effect

The Casimir-Lifshitz force acts between neutral material bodies and is due to the fluctuations (around zero) of the electrical polarizations of the bodies. This force is a macroscopic manifestation of the van der Waals forces between atoms and molecules. In addition to being of fundamental interest, the Casimir-Lifshitz force plays an important role in surface physics, nanotechnology and biophysics. There are two different approaches in the theory of this force. One is centered on the fluctuations inside the bodies, as the source of the fluctuational electromagnetic fields and forces. The second approach is based on finding the eigenmodes of the field, while the material bodies are assumed to be passive and non-fluctuating. In spite of the fact that both approaches have a long history, there are still some misconceptions in the literature. In particular, there are claims that (hypothetical) materials with a strictly real dielectric function $\varepsilon(\omega)$ can give rise to fluctuational Casimir-Lifshitz forces. We review and compare the two approaches, using the simple example of the force in the absence of retardation. We point out that also in the second (the "field-oriented") approach one cannot avoid introducing an infinitesimal imaginary part into the dielectric function, i.e. introducing some dissipation. Furthermore, we emphasize that the requirement of analyticity of $ \varepsilon(\omega)$ in the upper half of the complex $\omega$ plane is not the only one for a viable dielectric function. There are other requirements as well. In particular, models that use a strictly real $\varepsilon(\omega)$ (for all real positive $\omega)$ are inadmissible and lead to various contradictions and inconsistencies. Specifically, we present a critical discussion of the "dissipation-less plasma model". Our emphasis is not on the most recent developments in the field but on some conceptual, not fully resolved issues.

Zeptometer Metrology Using the Casimir Effect

In this paper, we discuss using the Casimir force in conjunction with a MEMS parametric amplifier to construct a quantum displacement amplifier. Such a mechanical amplifier converts DC displacements into much larger AC oscillations via the quantum gain of the system which, in some cases, can be a factor of a million or more. This would allow one to build chip scale metrology systems with zeptometer positional resolution. This approach leverages quantum fluctuations to build a device with a sensitivity that can’t be obtained with classical systems.

Casimir effect with one large extra dimension

In this work, I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the [Formula: see text]-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three-dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension could be used as an effective tool to explore the existence of large compactified extra dimensions.

Two Kinds of Vacuum in Casimir Effect

The Casimir effect is one observable of the existence of the vacuum energy, i.e. the existence of vacuum electromagnetic field. The meaning of this word "vacuum" is physical vacuum, not technology vacuum. Then, we say that the change in the vacuum structure enforced by the plates. There are two kinds of vacuum, one is usual vacua or free vacua (outside the plates). Another is the negative energy vacua (inside the plates), and the refraction index less than 1(n<1). That cause a change in the light speed for electromagnetic waves propagating perpendicular to the plates: △c/c1.6×10-60d-4, and d is the plate distance. When d=10-9m(1nm), △c=10-24c. Then, a two-loop QED effect cause the phase and group velocities of an electromagnetic wave to slightly exceed c. Though the difference are very small, that raise interesting matters of principle. The focus of this paper is to improve the understanding of the nature of quantum vacuum. In the past, to say that "vacuum is not empty" was already a criticism and subversion of classical physics. Now it seems doubly strange to say that there is a negative energy vacuum that is "empty"than the normal physical vacuum. But these theories are rigorously justified; Casimir effect can create an environment with refractive index less than 1(n<1) and lead to the appearance of superluminality, which is one of the representations of "quantum superluminality". These advances in basic science will certainly open up new fields of application, In short, it is not the Casimir structure that creates the quantum vacuum, but the structure that makes the quantum vacuum "emerge"in a clever way as a perceptible physical reality. This is truly a scientific achievement.

Casimir Effect between Superconducting Plates in the Mixed State

The Casimir effect between type-II superconducting plates in the coexisting phase of a superconducting phase and a normal phase is investigated. The dependence of the optical conductivity of the superconducting plates on the external magnetic field is described in terms of the penetration depth of the incident electromagnetic field, and the permittivity along the imaginary axis is represented by a linear combination of the permittivities for the plasma model and Drude models. The characteristic frequency in each model is determined using the force parameters for the motion of the magnetic field vortices. The Casimir force between parallel YBCO plates in the mixed state is calculated, and the dependence on the applied magnetic field and temperature is considered.