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K. A. Milton

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

At least 19 recordsLinked to original sources
arXiv2022

Effect of excess charge carriers and fluid medium on the magnitude and the sign of the Casimir-Lifshitz torque

Last year, we reported a perturbative theory of the Casimir-Lifshitz torque between planar biaxially anisotropic materials in the retarded limit [Phys. Rev. Lett. {\bf 120}, 131601 (2018)], which is applied here to study the change of sign and magnitude of the torque with separation distance in biaxial black phosphorus having excess charge carriers. The study is carried out both in vacuum as well as in a background fluid medium. The presence of extra charge carriers and that of an intervening fluid medium are both found to promote enhancement of the magnitude of the torque between identical slabs. The degree of enhancement of the magnitude of torque increases not only with an increased carrier concentration but also with separation distance. In the non-identical case when different planes of anisotropic black phosphorus face each other, owing to the non-monotonic characteristic of the sign-reversal effect of the torque, the enhancement by carrier addition and intervening medium also becomes non-monotonic with distance. In the presence of a background medium, the non-monotonic degree of enhancement of the torque with distance is observed even between identical slabs.

cond-mat.mes-hall↗
arXiv2018

Renormalization for a Scalar Field in an External Scalar Potential

The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here this is demonstrated in detail for two different models of the field-potential coupling. here is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully interacting quantum field theories; these terms are finite but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply rising smooth potential.

hep-th↗
arXiv2017

Casimir Self-Entropy of a Spherical Electromagnetic $δ$-Function Shell

In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic $δ$-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The TE self-entropy is negative as expected, but the TM self-entropy requires ultraviolet and infrared subtractions, and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes.

hep-th↗
arXiv2016

Casimir Self-Entropy of an Electromagnetic Thin Sheet

Casimir entropies due to quantum fluctuations in the interaction between electrical bodies can often be negative, either caused by dissipation or by geometry. Although generally such entropies vanish at zero temperature, consistent with the third law of thermodynamics (the Nernst heat theorem), there is a region in the space of temperature and separation between the bodies where negative entropy occurs, while positive interaction entropies arise for large distances or temperatures. Systematic studies on this phenomenon in the Casimir-Polder interaction between a polarizable nanoparticle or atom and a conducting plate in the dipole approximation have been given recently. Since the total entropy should be positive according to the second law of thermodynamics, we expect that the self-entropy of the bodies would be sufficiently positive as to overwhelm the negative interaction entropy. This expectation, however, has not been explicitly verified. Here we compute the self-entropy of an electromagnetic $δ$-function plate, which corresponds to a perfectly conducting sheet in the strong coupling limit. The transverse electric contribution to the self-entropy is negative, while the transverse magnetic contribution is larger and positive, so the total self-entropy is positive. However, this self-entropy vanishes in the strong-coupling limit. In that case, it is the self-entropy of the nanoparticle that is just sufficient to result in a nonnegative total entropy.

hep-th↗
arXiv2016

The Reality of Casimir Friction

For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with phenomena, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.

quant-ph↗
arXiv2015

The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of non-magnetic materials (Guerout et al, Phys. Rev. E 90 042125), we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.

quant-ph↗
arXiv2015

Casimir Friction Between Polarizable Particle and Half-Space with Radiation Damping and Image Damping at Zero Temperature

Casimir friction between a polarizable particle and a semi-infinite space is a delicate physical phenomenon, as it concerns the interaction between a microscopic quantum particle and a semi-infinite reservoir. Not unexpectedly, results obtained in the past about the friction force obtained via different routes are sometimes, at least apparently, wildly different from each other. Recently, we considered the Casimir friction force for two dielectric semi-infinite plates moving parallel to each other [J. S. Høye and I. Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], and managed to get essential agreement with results obtained by Pendry (1997), Volokitin and Persson (2007), and Barton (2011). Our method was based upon use of the Kubo formalism. In the present paper we focus on the interaction between a polarizable particle and a dielectric half-space again, and calculate the friction force using the same basic method as before. The new ingredient in the present analysis is that we take into account radiative damping, and derive the modifications thereof. Some comparisons are also made with works from others. Essential agreement with the results of Intravaia, Behunin, and Dalvit can also be achieved using the modification of the atomic polarizability by the metallic plate.

quant-ph↗
arXiv2015

Schwinger's Quantum Action Principle: From Dirac's formulation through Feynman's path integrals, the Schwinger-Keldysh method, quantum field theory, to source theory

Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from Schwinger's lectures over four decades, the continuity of concepts, such as that of Green's functions, becomes apparent.

quant-ph↗
arXiv2014

Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors

We carefully re-examine the conditions of validity for the consistent derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors. We recover the usual expression for the lossy Drude model, but not for the lossless plasma model. We give an interpretation of this new result in terms of the modes associated with the Foucault currents which play a role in the limit of vanishing losses, in contrast to common expectations.

quant-ph↗
arXiv2014

Synthetic versus Dirac monopoles

In some recent experiments the distinction between synthetic magnetic monopoles and Dirac monopoles has been blurred. A case in point is the work in a letter by Ray {\it et al.} [arXiv:1408.3133] in which a beautiful experiment is reported but claims with regard to Dirac monopoles are misleading.

hep-th↗
arXiv2014

Negative Casimir Entropies in Nanoparticle Interactions

Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically polarizable nanoparticles or atoms, which need not be isotropic, and between such a small object and a conducting plate. Negative entropy can occur even between two perfectly conducting spheres, between two electrically polarizable nano-particles if there is sufficient anisotropy, between a perfectly conducting sphere and a Drude sphere,and between a sufficiently anisotropic electrically polarizable nano-particle and a transverse magnetic conducting plate.

quant-ph↗
arXiv2014

Schwinger's Quantum Action Principle. I. From Dirac's Formulation through Feynman's Path Integrals to the Schwinger-Keldysh Method

Starting from the earlier notions of stationary action principles, we show how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.

physics.hist-ph↗
arXiv2014

Schwinger's Approach to Einstein's Gravity and Beyond

Julian Schwinger (1918--1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle-physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved spacetime. This note provides a brief summary of his contributions and attitudes toward the subject of gravity.

physics.hist-ph↗
arXiv2014

How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energy-momentum-stress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent ($δ$-function) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time point-split regulation parameters, and obtain well-defined contributions to the self- energy of each plate, and the interaction energy between the plates. (This self-energy does not vanish even in the conformally-coupled, strong-coupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this well-defined system is then investigated, and it is verified that the equivalence principle is satisfied.

hep-th↗
arXiv2012

Scalar Casimir Energies of Tetrahedra and Prisms

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 edges, 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. Cubic, rectangular parallelepipedal, triangular prismatic, and spherical geometries are also revisited. Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. Smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed.

hep-th↗
arXiv2012

Thermal Issues in Casimir Forces Between Conductors and Semiconductors

The Casimir effect between metal surfaces has now been well-verified at the few-percent level experimentally. However, the temperature dependence has never been observed in the laboratory, since all experiments are conducted at room temperature. The temperature dependence for the related Casimir-Polder force between an atom and a bulk material has, in contrast, been observed between a BEC and a silica substrate, with the environment and the silica held at different temperatures. There is a controversy about the temperature dependence for the force between metals, having to do with the magnitude of the linear temperature term for both low and high temperature, the latter being most prominent at large distances. There are also related anomalies pertaining to semiconductors. The status of this controversy, and of the relevant experiments, are reviewed in this report.

hep-th↗