arXiv subjects

F. Ravndal

Publications and source records attributed to F. Ravndal.

10 recordsLinked to original sources

arXiv2007

Electromagnetic Casimir energy with extra dimensions

We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can be mapped upon the corresponding problem with a massless, scalar field satisfying respectively Dirichlet or Neumann boundary conditions. The pressure between the plates is constant while the energy density is found to diverge at the boundaries when there are extra dimensions. This can be related to the fact that Maxwell theory is then no longer conformally invariant. A similar behavior is known for the scalar field where a constant energy density consistent with the pressure can be obtained by improving the energy-momentum tensor with the Huggins term. This is not possible for the Maxwell field. However, the change in the energy-momentum tensor with distance between boundaries is finite in all cases.

quant-ph↗

arXiv2007

Resolution of an apparent inconsistency in the electromagnetic Casimir effect

The vacuum expectation value of the electromagnetic energy-momentum tensor between two parallel plates in spacetime dimensions D > 4 is calculated in the axial gauge. While the pressure between the plates agrees with the global Casimir force, the energy density is divergent at the plates and not compatible with the total energy which follows from the force. However, subtracting the divergent self-energies of the plates, the resulting energy is finite and consistent with the force. In analogy with the corresponding scalar case for spacetime dimensions D > 2, the divergent self-energy of a single plate can be related to the lack of conformal invariance of the electromagnetic Lagrangian for dimensions D > 4.

hep-ph↗

arXiv2005

Black-body radiation in extra dimensions

The general form of the Stefan-Boltzmann law for the energy density of black-body radiation is generalized to a spacetime with extra dimensions using standard kinetic and thermodynamic arguments. From statistical mechanics one obtains an exact formula. In a field-theoretic derivation, the Maxwell field must be quantized. The notion of electric and magnetic fields is different in spacetimes with more than four dimensions. While the energy-momentum tensor for the Maxwell field is traceless in four dimensions, it is not so when there are extra dimensions. But it is shown that its thermal average is traceless and in agreement with the thermodynamic results.

quant-ph↗

arXiv2002

Exponentially Large Extra Dimensions

We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii which are naturally exponentially large, $r \sim \ell \exp [(4π)^3/g^2]$, where $\ell$ is a microscopic physics scale and $g$ is the (dimensionless) cubic coupling constant. The resulting radion mode of the metric becomes a very light degree of freedom whose mass, $m \sim 1/(M_p r^2)$ is stable under radiative corrections. For $1/r \sim 10^{-3}$ eV the radion is extremely light, $m \sim 10^{-33}$ eV. Its couplings cause important deviations from General Relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.

hep-th↗

arXiv2001

Natural Quintessence and Large Extra Dimensions

We examine the late-time (nucleosynthesis and later) cosmological implications of brane-world scenarios having large (millimeter sized) extra dimensions. In particular, recent proposals for understanding why the extra dimensions are so large in these models indicate that moduli like the radion appear (to four-dimensional observers) to be extremely light, with a mass of order 10^{-33} eV, allowing them to play the role of the light scalar of quintessence models. The radion-as-quintessence solves a long-standing problem since its small mass is technically natural, in that it is stable against radiative corrections. Its challenges are to explain why such a light particle has not been seen in precision tests of gravity, and why Newton's constant has not appreciably evolved since nucleosynthesis. We find the couplings suggested by stabilization models can provide explanations for both of these questions. We identify the features which must be required of any earlier epochs of cosmology in order for these explanations to hold.

astro-ph↗

arXiv1997

Thermodynamics of a weakly interacting Bose-Einstein gas

The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the standard ground state energy and pressureas function of the particle density. At finite temperatures it is found necessary to include ring corrections to the one-loop result in order to satisfy the Goldstone theorem. It is natural to introduce an effective chemical potential directly related to the order parameter and which uniformly decreases with increasing temperatures. This is in contrast to the the ordinary chemical potential which peaks at the critical temperature. The resulting thermodynamics in the condensed phase at very low temperatures is found to be the same as in the Bogoliubov approximation where the degrees of freedom are given by the Goldstone bosons. At higher temperatures the ring corrections dominate and result in a critical temperature unaffected by the interaction.

cond-mat.stat-mech↗

arXiv1996

A more accurate analysis of Bose-Einstein condensation in harmonic traps

Using the Euler-Maclaurin summation we calculate analytically the internal energy for non-interacting bosons confined within a harmonic oscillator potential. The specific heat shows a sharp $λ$-like peak indicating a condensation into the ground state at a well-defined transition temperature. Full agreement is obtained with direct numerical calculation of the same quantities. When the number of trapped particles is very large and at temperatures near and above the transition temperature, the results also agree with previous approximate calculations. At extremely low temperatures both the specific heat and the number of particles excited from the condensate are exponentially suppressed.

cond-mat↗

arXiv1995

Bose-Einstein condensation in the harmonic oscillator potential

The Bose-Einstein condensation of a dilute gas of rubidium-87 atoms was achieved by cooling a small number of atoms in a magnetic trap. The effective potential of the trap is to lowest order harmonic and under these conditions we estimate the critical temperature and the heat capacity of an ideal gas of Bose particles. Previously this has been estimated within the semiclassical approximation. However, because of the small number of atoms, the resulting $T_c$ deviates slightly from our result obtained by exact numerical calculations. For the gap of the heat capacity at the transition point the deviation is $20\%$.

cond-mat↗

arXiv1994

Ideal quantum gases in two dimensions

Thermodynamic properties of non-relativistic bosons and fermions in two spatial dimensions and without interactions are derived. All the virial coefficients are the same except for the second, for which the signs are opposite. This results in the same specific heat for the two gases. Existing equations of state for the free anyon gas are also discussed and shown to break down at low temperatures or high densities.

hep-th↗

arXiv1993

Scale anomalies in non-relativistic field theories in 2+1 dimensions

{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor follows directly. It is also similarly derived when the bosons have an additional Chern-Simons interaction. In the special case of anyons, the scale anomaly vanishes to one-loop order in the effective potential and also to second order in the statistical angle.

hep-th↗