Brownian motion of a charged test particle near a reflecting boundary at finite temperature

We discuss the random motion of charged test particles driven by quantum electromagnetic fluctuations at finite temperature in both the unbounded flat space and flat spacetime with a reflecting boundary and calculate the mean squared fluctuations in the velocity and position of the test particle. We show that typically the random motion driven by the quantum fluctuations is one order of magnitude less significant than that driven by thermal noise in the unbounded flat space. However, in the flat space with a reflecting plane boundary, the random motion of quantum origin can become much more significant than that of thermal origin at very low temperature.Comment: 11 pages,no figures, Revtex

Casimir force on a piston

We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L x b rectangular box, divided by a movable partition (piston) into two compartments of dimensions a x b and (L-a) x b. We compute the Casimir force on the piston in the limit L -> infinity. Regardless of the value of a/b, the piston is attracted to the nearest end of the box. Asymptotic expressions for the Casimir force on the piston are derived for a << b and a >> b.Comment: 10 pages, 1 figure. Final version, accepted for publication in Phys. Rev.

Focusing Vacuum Fluctuations II

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is further developed in the context of a geometric optics approximation. We extend results in a previous paper to more general geometries, and also correct an error in one section of that paper. We calculate the mean squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean squared fields. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.Comment: 26 pages, 15 figures; additional discussion added in Sects. IV and I

A new "polarized version" of the Casimir Effect is measurable

We argue that the exactly computable, angle dependent, Casimir force between parallel plates with different directions of conductivity can be measured.Comment: One Figure, 11 page

Onset voltage shift due to non-zero Landau ground state level in coherent magnetotransport

Coherent electron transport in double-barrier heterostructures with parallel electric and magnetic fields is analyzed theoretically and with the aid of a quantum simulator accounting for 3-dimensional transport effects. The onset-voltage shift induced by the magnetic field in resonant tunneling diodes, which was previously attributed to the cyclotron frequency $w_c$ inside the well is found to arise from an upward shift of the non-zero ground (lowest) Landau state energy in the entire quantum region where coherent transport takes place. The spatial dependence of the cyclotron frequency is accounted for and verified to have a negligible impact on resonant tunneling for the device and magnetic field strength considered. A correction term for the onset-voltage shift arising from the magnetic field dependence of the chemical potential is also derived. The Landau ground state with its nonvanishing finite harmonic oscillator energy $\hbar w_c /2$ is verified however to be the principal contributor to the onset voltage shift at low temperatures.Comment: 13 pages, and 3 figures. Accepted for publication in Phys. Rev.

Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time

Charged scalar field is quantized in the background of a static d-2 - brane which is a core of the magnetic flux lines in flat d+1 - dimensional space-time. We find that vector potential of the magnetic core induces the energy-momentum tensor in the vacuum. The tensor components are periodic functions of the brane flux and holomorphic functions of space dimension. The dependence on the distance from the brane and on the coupling to the space-time curvature scalar is comprehensively analysed.Comment: 32 pages, 3 figures, journal version, some references adde

Spontaneous emission between an unusual pair of plates

We compute the modification in the spontaneous emission rate for a two-level atom when it is located between two parallel plates of different nature: a perfectly conducting plate $(\epsilon\to \infty)$ and an infinitely permeable one $(\mu\to \infty)$. We also discuss the case of two infinitely permeable plates. We compare our results with those found in the literature for the case of two perfectly conducting plates.Comment: latex file 4 pages, 4 figure

Calculating Casimir Energies in Renormalizable Quantum Field Theory

Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been studied by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$ not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for $D\ne1$. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in $D$ and three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B and Appendix, and other minor correction

Fluctuations of the Retarded Van der Waals Force

The retarded Van der Waals force between a polarizable particle and a perfectly conducting plate is re-examined. The expression for this force given by Casimir and Polder represents a mean force, but there are large fluctuations around this mean value on short time scales which are of the same order of magnitude as the mean force itself. However, these fluctuations occur on time scales which are typically of the order of the light travel time between the atom and the plate. As a consequence, they will not be observed in an experiment which measures the force averaged over a much longer time. In the large time limit, the magnitude of the mean squared velocity of a test particle due to this fluctuating Van der Waals force approaches a constant, and is similar to a Brownian motion of a test particle in an thermal bath with an effective temperature. However the fluctuations are not isotropic in this case, and the shift in the mean square velocity components can even be negative. We interpret this negative shift to correspond to a reduction in the velocity spread of a wavepacket. The force fluctuations discussed in this paper are special case of the more general problem of stress tensor fluctuations. These are of interest in a variety of areas fo physics, including gravity theory. Thus the effects of Van der Waals force fluctuations serve as a useful model for better understanding quantum effects in gravity theory.Comment: 14 pages, no figure

Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.Comment: 8 pages, 4 figures, Accepted for publication in Eur. Phys. J.