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K. A. Milton

Publications and source records attributed to K. A. Milton.

At least 37 records · Page 2Linked to original sources
arXiv2011

Scalar Casimir Energies of Tetrahedra

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the corners, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Dirichlet and Neumann boundary conditions are considered and systematic behavior of the energy in terms of geometric invariants is explored.

hep-th↗
arXiv2011

Repulsive Casimir Effects

Like Casimir's original force between conducting plates in vacuum, Casimir forces are usually attractive. But repulsive Casimir forces can be achieved in special circumstances. These might prove useful in nanotechnology. We give examples of when repulsive quantum vacuum forces can arise with conducting materials.

hep-th↗
arXiv2010

Casimir Energies of Cylinders: Universal Function

New exact results are given for the interior Casimir energies of infinitely long waveguides of triangular cross section (equilateral, hemiequilateral, and isosceles right triangles). Results for cylinders of rectangular cross section are rederived. In particular, results are obtained for interior modes belonging to Dirichlet and Neumann boundary conditions (TM and TE modes). These results are expressed in rapidly convergent series using the Chowla-Selberg formula, and in fact may be given in closed form, except for general rectangles. The energies are finite because only the first three heat-kernel coefficients can be nonzero for the case of polygonal boundaries. What appears to be a universal behavior of the Casimir energy as a function of the shape of the regular or quasi-regular cross-sectional figure is presented. Furthermore, numerical calculations for arbitrary right triangular cross sections suggest that the universal behavior may be extended to waveguides of general polygonal cross sections. The new exact and numerical results are compared with the proximity force approximation (PFA).

hep-th↗
arXiv2009

Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media

The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situation. We also discuss the appropriate choice of the electromagnetic energy-momentum tensor.

hep-th↗
arXiv2009

Nanowire atomchip traps for sub-micron atom-surface distances

We present an analysis of magnetic traps for ultracold atoms based on current-carrying wires with sub-micron dimensions. We analyze the physical limitations of these conducting wires, as well as how such miniaturized magnetic traps are affected by the nearby surface due to tunneling to the surface, surface thermal noise, electron scattering within the wire, and the Casimir-Polder force. We show that wires with cross sections as small as a few tens of nanometers should enable robust operating conditions for coherent atom optics (e.g. tunneling barriers for interferometry). In particular, trap sizes on the order of the deBroglie wavelength become accessible, based solely on static magnetic fields, thereby bringing the atomchip a step closer to fulfilling its promise of a compact device for complex and accurate quantum optics with ultracold atoms.

quant-ph↗
arXiv2009

Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols

Rectangular cavities are solvable models that nevertheless touch on many of the controversial or mysterious aspects of the vacuum energy of quantum fields. This paper is a thorough study of the two-dimensional scalar field in a rectangle by the method of images, or closed classical (or optical) paths, which is exact in this case. For each point r and each specularly reflecting path beginning and ending at r, we provide formulas for all components of the stress tensor T_{μν}(r), for all values of the curvature coupling constant ξand all values of an ultraviolet cutoff parameter. Arbitrary combinations of Dirichlet and Neumann conditions on the four sides can be treated. The total energy is also investigated, path by path. These results are used in an attempt to clarify the physical reality of the repulsive (outward) force on the sides of the box predicted by calculations that neglect both boundary divergences and the exterior of the box. Previous authors have studied "piston" geometries that avoid these problems and have found the force to be attractive. We consider a "pistol" geometry that comes closer to the original problem of a box with a movable lid. We find again an attractive force, although its origin and detailed behavior are somewhat different from the piston case. However, the pistol (and the piston) model can be criticized for extending idealized boundary conditions into short distances where they are physically implausible. Therefore, it is of interest to see whether leaving the ultraviolet cutoff finite yields results that are more plausible. We then find that the force depends strongly on a geometrical parameter; it can be made repulsive, but only by forcing that parameter into the regime where the model is least convincing physically.

hep-th↗
arXiv2008

How Does Quantum Vacuum Energy Accelerate?

We show that Casimir energy for a configuration of parallel plates gravitates according to the equivalence principle both for the finite and divergent parts. This shows that the latter can be absorbed by a process of renormalization.

hep-th↗
arXiv2008

Recent Developments in the Casimir Effect

In this talk I review various developments in the past year concerning quantum vacuum energy, the Casimir effect. In particular, there has been continuing controversy surrounding the temperature correction to the Lifshitz formula for the Casimir force between real materials, be they metals or semiconductors. Consensus has emerged as to how Casimir energy accelerates in a weak gravitational field; quantum vacuum energy, including the divergent parts which renormalize the masses of the Casimir plates, accelerates indeed according to the equivalence principle. Significant development has been forthcoming in applying the multiple scattering formalism to describe the interaction between nontrivial objects. In weak coupling, closed-form expressions for the Casimir force between the bodies, which for example reveal significant discrepancies from the naive proximity force approximation, can be achieved in many cases.

hep-th↗
arXiv2008

Casimir Energies: Temperature Dependence, Dispersion, and Anomalies

Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy $W_{\rm disp}$ when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form $d[ωε(ω)] /dω$ and $d[ωμ(ω)] /dω$. We find that, as $W_{\rm disp}$ refers thermodynamically to a non-closed physical system, it is {\it not} to be identified with the internal thermodynamic energy $U$ following from the free energy $F$, or the electromagnetic energy $W$, when the last-mentioned quantities are calculated without such dispersive derivatives. To arrive at this conclusion, we adopt a model in which the system is a capacitor, linked to an external self-inductance $L$ such that stationary oscillations become possible. Therewith the model system becomes a non-closed one. As an introductory step, we review the meaning of the nondispersive energies, $F, U,$ and $W$. As a final topic, we consider an anomaly connected with local surface divergences encountered in Casimir energy calculations for higher spacetime dimensions, $D>4$, and discuss briefly its dispersive generalization. This kind of application is essentially a generalization of the treatment of Alnes {\it et al.} [J. Phys. A: Math. Theor. {\bf 40}, F315 (2007)] to the case of a medium-filled cavity between two hyperplanes.

quant-ph↗
arXiv2008

Coulomb Resummation and Monopole Masses

The relativistic Coulomb resummation factor suggested by I.L. Solovtsov is used to reanalyze the mass limits obtained for magnetic monopoles which might have been produced at the Fermilab Tevatron. The limits given by the Oklahoma experiment (Fermilab E882) are pushed close to the unitary bounds, so that the lower limits on monopole masses are increased from around 250 GeV to about 400 GeV.

hep-ph↗
arXiv2006

Local and Global Casimir Energies in a Green's Function Approach

The effects of quantum fluctuations in fields confined by background configurations may be simply and transparently computed using the Green's function approach pioneered by Schwinger. Not only can total energies and surface forces be computed in this way, but local energy densities, and in general, all components of the vacuum expectation value of the energy-momentum tensor may be calculated. For simple geometries this approach may be carried out exactly, which yields insight into what happens in less tractable situations. In this talk I will concentrate on the example of a scalar field in a circular cylindrical delta-function background. This situation is quite similar to that of a spherical delta-function background. The local energy density in these cases diverges as the surface of the background is approached, but these divergences are integrable. The total energy is finite in strong coupling, but in weak coupling a divergence occurs in third order. This universal feature is shown to reflect a divergence in the energy associated with the surface, the integrated local energy density within the shell itself, which surface energy should be removable by a process of renormalization.

hep-th↗
arXiv2006

Julian Schwinger: Nuclear Physics, the Radiation Laboratory, Renormalized QED, Source Theory, and Beyond

Julian Schwinger's influence on twentieth century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and Sin-itiro Tomonaga. But although this triumph was undoubtedly his most heroic work, his legacy lives on chiefly through subtle and elegant work in classical electrodynamics, quantum variational principles, proper-time methods, quantum anomalies, dynamical mass generation, partial symmetry, and more. Starting as just a boy, he rapidly became the pre-eminent nuclear physicist in the late 1930s, led the theoretical development of radar technology at MIT during World War II, and then, soon after the war, conquered quantum electrodynamics, and became the leading quantum field theorist for two decades, before taking a more iconoclastic route during his last quarter century.

physics.hist-ph↗
arXiv2006

Julian Schwinger (1918-1994)

Julian Schwinger's influence on Twentieth Century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and Sin-itiro Tomonaga. But although this triumph was undoubtedly his most heroic accomplishment, his legacy lives on chiefly through subtle and elegant work in classical electrodynamics, quantum variational principles, proper-time methods, quantum anomalies, dynamical mass generation, partial symmetry, and more. Starting as just a boy, he rapidly became the pre-eminent nuclear physicist in the late 1930s, led the theoretical development of radar technology at MIT during World War II, and then, soon after the war, conquered quantum electrodynamics, and became the leading quantum field theorist for two decades, before taking a more iconoclastic route during his last quarter century.

physics.hist-ph↗
arXiv2006

What is the Temperature Dependence of the Casimir Effect?

There has been recent criticism of our approach to the Casimir force between real metallic surfaces at finite temperature, saying it is in conflict with the third law of thermodynamics and in contradiction with experiment. We show that these claims are unwarranted, and that our approach has strong theoretical support, while the experimental situation is still unclear.

quant-ph↗
arXiv2006

Theoretical and Experimental Status of Magnetic Monopoles

The Tevatron has inspired new interest in the subject of magnetic monopoles. First there was the 1998 D0 limit on the virtual production of monopoles, based on the theory of Ginzburg and collaborators. In 2000 and 2004 results from an experiment (Fermilab E882) searching for real magnetically charged particles bound to elements from the CDF and D0 detectors were reported. The strongest direct experimental limits, from the CDF collaboration, have been reported in 2005. Less strong, but complementary, limits from the H1 collaboration at HERA were reported in the same year. Interpretation of these experiments also require new developments in theory. Earlier experimental and observational constraints on point-like (Dirac) and non-Abelian monopoles were given from the 1970s through the 1990s, with occasional short-lived positive evidence for such exotic particles reported. The status of the experimental limits on monopole masses will be reported, as well as the limitation of the theory of magnetic charge at present.

hep-ex↗
arXiv2006

Surface Divergences and Boundary Energies in the Casimir Effect

Although Casimir, or quantum vacuum, forces between distinct bodies, or self-stresses of individual bodies, have been calculated by a variety of different methods since 1948, they have always been plagued by divergences. Some of these divergences are associated with the volume, and so may be more or less unambiguously removed, while other divergences are associated with the surface. The interpretation of these has been quite controversial. Particularly mysterious is the contradiction between finite total self-energies and surface divergences in the local energy density. In this paper we clarify the role of surface divergences.

hep-th↗
arXiv2005

An analytic method of describing $R$-related quantities in QCD

A model based on the analytic approach to QCD, involving a summation of threshold singularities and taking into account the nonperturbative character of the light quark masses, is applied to find hadronic contributions to different physical quantities. It is shown that the suggested model allows us to describe well such objects as the hadronic contribution to the anomalous magnetic moment of the muon, the ratio of hadronic to leptonic $τ$-decay widths in the vector channel, the Adler $D$-function, the smeared $R_Δ$-function, and the hadronic contribution to the evolution of the fine structure constant.

hep-ph↗