The Casimir Effect

After a review of the standard calculation of the Casimir force between two metallic plates at zero and non-zero temperatures, we present the study of microscopic models to determine the large-distance asymptotic force in the high-temperature regime. Casimir's conducting plates are modelized by plasmas of interacting charges at temperature T. The charges are either classical, or quantum-mechanical and coupled to a (classical) radiation field. In these models, the force obtained is twice weaker than that arising from standard treatments neglecting the microscopic charge fluctutations inside the bodies. The enforcement of inert boundary conditions on the field in the usual calculations turns out to be inadequate in this regime. Other aspects of dispersion forces are also reviewed. The status of (non-retarded) van der Waals-London forces in a dilute medium of non-zero temperature and density is investigated. In a proper scaling regime called the atomic limit (high dilution and low temperature), one is able to give the exact large-distance atomic correlations up to exponentially small terms as T->0. Retarded van der Waals forces and forces between dielectric bodies are also reviewed. Finally, the Casimir effect in critical phenomena is addressed by considering the free Bose gas. It is shown that the grand-canonical potential of the gas in a slab at the critical value of the chemical potential has finite size corrections of the standard Casimir type. They can be attributed to the existence of long-range order generated by gapless excitations in the phase with broken continuous symmetry.Comment: Lecture notes prepared for the proceedings of the 1st Warsaw School of Statistical Physics, Kazimierz, Poland, June 2005. To appear in Acta Physica Polonica (2006). 52 pages, 0 figures. Available at http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p2503.pd

A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse

We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation. This model is applied to simulate the spatio-temporal evolution of a human midshaft femur scan subjected to two deregulating circumstances: (i) osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to endocortical bone loss, cortical wall thinning and expansion of the medullary cavity, in accordance with experimental findings. Our model suggests that these observations are attributable to a large extent to the influence of the microstructure on bone turnover rate. Mechanical adaptation is found to help preserve intracortical bone matrix near the periosteum. Moreover, it leads to non-uniform cortical wall thickness due to the asymmetry of macroscopic loads introduced by the bending moment. The effect of mechanical adaptation near the endosteum can be greatly affected by whether the mechanical stimulus includes stress concentration effects or not.Comment: 25 pages, 10 figure

The Casimir force at high temperature

The standard expression of the high-temperature Casimir force between perfect conductors is obtained by imposing macroscopic boundary conditions on the electromagnetic field at metallic interfaces. This force is twice larger than that computed in microscopic classical models allowing for charge fluctuations inside the conductors. We present a direct computation of the force between two quantum plasma slabs in the framework of non relativistic quantum electrodynamics including quantum and thermal fluctuations of both matter and field. In the semi-classical regime, the asymptotic force at large slab separation is identical to that found in the above purely classical models, which is therefore the right result. We conclude that when calculating the Casimir force at non-zero temperature, fluctuations inside the conductors can not be ignored.Comment: 7 pages, 0 figure

Testing the existence of optical linear polarization in young brown dwarfs

Linear polarization can be used as a probe of the existence of atmospheric condensates in ultracool dwarfs. Models predict that the observed linear polarization increases withthe degree of oblateness, which is inversely proportional to the surface gravity. We aimed to test the existence of optical linear polarization in a sample of bright young brown dwarfs, with spectral types between M6 and L2, observable from the Calar Alto Observatory, and cataloged previously as low gravity objects using spectroscopy. Linear polarimetric images were collected in I and R-band using CAFOS at the 2.2 m telescope in Calar Alto Observatory (Spain). The flux ratio method was employed to determine the linear polarization degrees. With a confidence of 3$\sigma$, our data indicate that all targets have a linear polarimetry degree in average below 0.69% in the I-band, and below 1.0% in the R-band, at the time they were observed. We detected significant (i.e. P/$\sigma$ $\le$ 3) linear polarization for the young M6 dwarf 2MASS J04221413+1530525 in the R-band, with a degree of $\mathrm{p^{*}}$ = 0.81 $\pm$ 0.17 %.Comment: Accepted for publication in MNRA

Small vs large dust grains in transitional disks: do different cavity sizes indicate a planet?

Transitional disks represent a short stage of the evolution of circumstellar material. Studies of dust grains in these objects can provide pivotal information on the mechanisms of planet formation. Dissimilarities in the spatial distribution of small (micron-size) and large (millimeter-size) dust grains have recently been pointed out. Constraints on the small dust grains can be obtained by imaging the distribution of scattered light at near-infrared wavelengths. We aim at resolving structures in the surface layer of transitional disks (with particular emphasis on the inner 10 - 50 AU), thus increasing the scarce sample of high resolution images of these objects. We obtained VLT/NACO near-IR high-resolution polarimetric differential imaging observations of SAO 206462 (HD135344B). This technique allows one to image the polarized scattered light from the disk without any occulting mask and to reach an inner working angle of 0.1''. A face-on disk is detected in H and Ks bands between 0.1'' and 0.9''. No significant differences are seen between the H and Ks images. In addition to the spiral arms, these new data allow us to resolve for the first time an inner cavity for small dust grains. The cavity size (about 28 AU) is much smaller than what is inferred for large dust grains from (sub)mm observations (39 to 50 AU). The interaction between the disk and potential orbiting companion(s) can explain both the spiral arm structure and the discrepant cavity sizes for small and large dust grains. One planet may be carving out the gas (and, thus, the small grains) at 28 AU, and generating a pressure bump at larger radii (39 AU), which holds back the large grains. We analytically estimate that, in this scenario, a single giant planet (with a mass between 5 and 15 Jupiter masses) at 17 to 20 AU from the star is consistent with the observed cavity sizes.Comment: 11 pages, 6 figures; accepted for publication in A&

Direct imaging constraints on planet populations detected by microlensing

Results from gravitational microlensing suggested the existence of a large population of free-floating planetary mass objects. The main conclusion from this work was partly based on constraints from a direct imaging survey. This survey determined upper limits for the frequency of stars that harbor giant exoplanets at large orbital separations. Aims. We want to verify to what extent upper limits from direct imaging do indeed constrain the microlensing results. We examine the current derivation of the upper limits used in the microlensing study and re-analyze the data from the corresponding imaging survey. We focus on the mass and semi-major axis ranges that are most relevant in context of the microlensing results. We also consider new results from a recent M-dwarf imaging survey as these objects are typically the host stars for planets detected by microlensing. We find that the upper limits currently applied in context of the microlensing results are probably underestimated. This means that a larger fraction of stars than assumed may harbor gas giant planets at larger orbital separations. Also, the way the upper limit is currently used to estimate the fraction of free-floating objects is not strictly correct. If the planetary surface density of giant planets around M-dwarfs is described as df_Planet ~ a^beta da, we find that beta ~ 0.5 - 0.6 is consistent with results from different observational studies probing semi-major axes between ~0.03 - 30 AU. Having a higher upper limit on the fraction of stars that may have gas giant planets at orbital separations probed by the microlensing data implies that more of the planets detected in the microlensing study are potentially bound to stars rather than free-floating. The current observational data are consistent with a rising planetary surface density for giant exoplanets around M-dwarfs out to ~30 AU.Comment: Accepted for publication in A&A as Research Note, 3 page

Microscopic theory of the Casimir force at thermal equilibrium: large-separation asymptotics

We present an entirely microscopic calculation of the Casimir force $f(d)$ between two metallic plates in the limit of large separation $d$. The models of metals consist of mobile quantum charges in thermal equilibrium with the photon field at positive temperature $T$. Fluctuations of all degrees of freedom, matter and field, are treated according to the principles of quantum electrodynamics and statistical physics without recourse to approximations or intermediate assumptions. Our main result is the correctness of the asymptotic universal formula f(d) \sim -\frac{\zeta(3) \kB T}{8\pi d^3}, $d\to\infty$. This supports the fact that, in the framework of Lifshitz' theory of electromagnetic fluctuations, transverse electric modes do not contribute in this regime. Moreover the microscopic origin of universality is seen to rely on perfect screening sum rules that hold in great generality for conducting media.Comment: 34 pages, 0 figures. New version includes restructured intro and minor typos correcte

Thermal quantum electrodynamics of nonrelativistic charged fluids

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It has still the $r^{-6}$ decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.Comment: 32 pages, 0 figures. 2nd versio

Equilibrium correlations in charged fluids coupled to the radiation field

We provide an exact microscopic statistical treatment of particle and field correlations in a system of quantum charges in equilibrium with a classical radiation field. Using the Feynman-Kac-Ito representation of the Gibbs weight, the system of particles is mapped onto a collection of random charged wires. The field degrees of freedom can be integrated out, providing an effective pairwise magnetic potential. We then calculate the contribution of the transverse field coupling to the large-distance particle correlations. The asymptotics of the field correlations in the plasma are also exactly determined.Comment: 31 pages, 0 figures. PACS 05.30.-d, 05.40.-a, 11.10.Wx. Changes: Improved comparison with existing literature on field correlations. Added Concluding Remarks. References update