The electromagnetic field near a dielectric half-space

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform non-dispersive dielectric. This gives predictions for the Casimir-Polder force on an atom in the `retarded' regime near a dielectric. We also find a positive energy density due to the electromagnetic field. This would lead, in the case of two parallel dielectric half-spaces, to a positive, separation-independent contribution to the energy density, besides the negative, separation-dependent Casimir energy. Rough estimates suggest that for a very wide range of cases, perhaps including all realizable ones, the total energy density between the half-spaces is positive.Comment: Latex2e, IOP macros, 15 pages, 2 eps figure

Kant's philosophy of the aesthetic and the philosophy of praxis

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Association for Economic and Social Analysis.This essay seeks to reconstruct the terms for a more productive engagement with Kant than is typical within contemporary academic cultural Marxism, which sees him as the cornerstone of a bourgeois model of the aesthetic. The essay argues that, in the Critique of Judgment, the aesthetic stands in as a substitute for the missing realm of human praxis. This argument is developed in relation to Kant's concept of reflective judgment that is in turn related to a methodological shift toward inductive and analogical procedures that help Kant overcome the dualisms of the first two Critiques. This reassessment of Kant's aesthetic is further clarified by comparing it with and offering a critique of Terry Eagleton's assessment of the Kantian aesthetic as synonymous with ideology

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators

In this paper, we consider one dimensional adiabatic quasi-periodic Schr\"{o}dinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion

The implications of noninertial motion on covariant quantum spin

It is shown that the Pauli-Lubanski spin vector defined in terms of curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2 particles in noninertial motion along a curved trajectory. The possibility of detecting this violation in muon decay experiments is explored, where the noninertial contribution to the decay rate becomes large for muon beams with large momenta and trajectories with radius of curvature approaching the muon's Compton wavelength scale. A new spacelike spin vector is derived from the Pauli-Lubanski vector that satisfies Lorentz invariance for both inertial and noninertial motion. In addition, this spin vector suggests a generalization for the classification of spin-1/2 particles, and has interesting properties that are applicable for both massive and massless particles.Comment: REVTeX file; 7 pages; 2 figures; slightly revised with new abstract; accepted for publication in Classical and Quantum Gravit

Total angular momentum from Dirac eigenspinors

The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away be the gravitational radiation is also derived.Comment: 34 pages, typos corrected, four references added, appearing in Class. Quantum Gra

The Central Region of Barred Galaxies: Molecular Environment, Starbursts, and Secular Evolution

Despite compelling evidence that stellar bars drive gas into the inner 1--2 kpc or circumnuclear (CN) region of galaxies, there are few large, high resolution studies of the CN molecular gas and star formation (SF). We study a sample of local barred non-starbursts and starbursts with high-resolution CO, optical, Ha, RC, Br-gamma, and HST data, and find the following. (1) The inner kpc of bars differs markedly the outer disk and hosts molecular gas surface densities Sigma-gas-m of 500-3500 Msun pc-2, gas mass fractions of 10--30 %, and epicyclic frequencies of several 100--1000 km s-1 kpc-1.Consequently, gravitational instabilities can only set in at high gas densities and grow on a short timescale (few Myr). This high density, short timescale, `burst' mode may explain why powerful starbursts tend to be in the CN region of galaxies. (2) We suggest that the variety in CO morphologies is due to different stages of bar-driven inflow. At late stages, most of the CN gas is inside the outer inner Lindblad resonance (OILR), and has predominantly circular motions. Across the sample, we find bar pattern speeds with upper limits of 43 to 115 km s-1 kpc-1 and OILR radii of > 500 pc. (3) Barred starbursts and non-starbursts have CN SFRs of 3--11 and 0.1--2 Msun yr-1, despite similar CN gas mass. Sigma-gas-m in the starbursts is larger (1000--3500 Msun pc-2) and close to the Toomre critical density over a large region. (4) Molecular gas makes up 10%--30% of the CN dynamical mass (6--30 x 10^9 Msun).In the starbursts, it fuels CN SFRs of 3--11 Msun yr-1, building young, massive, high V/sigma components. We present evidence for such a pseudo-bulge in NGC 3351. Implications for secular evolution along the Hubble sequence are discussed.Comment: Accepted by the Astrophysical Journal. Paper length reduced to fit within APJ page limits. Version of paper with high resolution figures is at http://www.as.utexas.edu/~sj/papers/ms-hires-sj05a.ps.g

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Bounds on negative energy densities in flat spacetime

We generalise results of Ford and Roman which place lower bounds -- known as quantum inequalities -- on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-negative sampling functions which are either compactly supported or decay rapidly at infinity. Our results hold in $d$-dimensional Minkowski space ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in 2-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference adde

Effective Area-Elasticity and Tension of Micro-manipulated Membranes

We evaluate the effective Hamiltonian governing, at the optically resolved scale, the elastic properties of micro-manipulated membranes. We identify floppy, entropic-tense and stretched-tense regimes, representing different behaviors of the effective area-elasticity of the membrane. The corresponding effective tension depends on the microscopic parameters (total area, bending rigidity) and on the optically visible area, which is controlled by the imposed external constraints. We successfully compare our predictions with recent data on micropipette experiments.Comment: To be published in Phys. Rev. Let

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde