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T. G. Philbin

Publications and source records attributed to T. G. Philbin.

36 records · Page 2Linked to original sources
arXiv2014

Jarzynski equality for a gas particle driven out of equilibrium

One particle in a classical perfect gas is driven out of equilibrium by changing its mass over a short time interval. The work done on the driven particle depends on its collisions with the other particles in the gas. This model thus provides an example of a non-equilibrium process in a system (the driven particle) coupled to an environment (the rest of the gas). We calculate the work done on the driven particle and compare the results to Jarzynski's equality relating a non-equilibrium work process to an equilibrium free-energy difference. The results for this model are generalised to the case of a system that is driven in one degree of freedom while interacting with the environment through other degrees of freedom.

cond-mat.stat-mech↗
arXiv2014

Making geometrical optics exact

Geometrical optics (GO) is widely used in studies of electromagnetic materials because of its ease of use compared to full-wave numerical simulations. Exact solutions for waves can, however, differ significantly from the GO approximation. In particular, effects that are "perfect" for waves cannot usually be derived using GO. Here we give a method for designing materials in which GO is exact for some waves. This enables us to find interesting analytical solutions for exact wave propagation in inhomogeneous media. Two examples of the technique are given: a material in which two point sources do not interfere, and a perfect isotropic cloak for waves from a point source. We also give the form of material response required for GO to be exact for all waves.

physics.optics↗
arXiv2014

Canonical quantization of electromagnetism in spatially dispersive media

We find the action that describes the electromagnetic field in a spatially dispersive, homogeneous medium. This theory is quantized and the Hamiltonian is diagonalized in terms of a continuum of normal modes. It is found that the introduction of nonlocal response in the medium automatically regulates some previously divergent results, and we calculate a finite value for the intensity of the electromagnetic field at a fixed frequency within a homogeneous medium. To conclude we discuss the potential importance of spatial dispersion in taming the divergences that arise in calculations of Casimir-type effects.

quant-ph↗
arXiv2014

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co- ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an "invisible disc" and "multipole" lenses.

physics.optics↗
arXiv2013

Generalized coherent states

In the coherent state of the harmonic oscillator, the probability density is that of the ground state subjected to an oscillation along a classical trajectory. Senitzky and others pointed out that there are states of the harmonic oscillator corresponding to an identical oscillatory displacement of the probability density of any energy eigenstate. These generalizations of the coherent state are rarely discussed, yet they furnish an interesting set of quantum states of light that combine features of number states and coherent states. Here we give an elementary account of the quantum optics of generalized coherent states.

quant-ph↗
arXiv2013

Lipkin's conservation law, Noether's theorem, and the relation to optical helicity

A simple conserved quantity for electromagnetic fields in vacuum was discovered by Lipkin in 1964. In recent years this "zilch" has been used as a measure of the chirality of light. The conservation of optical zilch is here derived from a simple symmetry of the standard electromagnetic action. The symmetry transformation allows the identification of circularly polarized plane waves as zilch eigenstates. The same symmetry is present for electromagnetism in a homogeneous, dispersive medium, allowing the derivation of the zilch density and flux in such a medium. Optical helicity density and flux are also derived for a homogeneous, dispersive medium. For monochromatic beams in vacuum, optical zilch is proportional to optical helicity. This monochromatic zilch-helicity relation acquires a factor of the square of the phase index in a dispersive medium.

physics.optics↗
arXiv2012

Optical angular momentum in dispersive media

The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum of $\pm\hbar$ per energy $\hbarω$, as in vacuum. This result demonstrates the non-trivial interplay of dispersive contributions to optical angular momentum and energy.

physics.optics↗
arXiv2012

Electromagnetic energy-momentum in dispersive media

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The momentum density is not given by the familiar Minkowski expression $\mathbf{D}\times\mathbf{B}$, even for time-averaged monochromatic fields. The results are unaffected by the debate over momentum balance in light-matter interactions.

physics.optics↗
arXiv2012

Quantum dynamics of the damped harmonic oscillator

The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.

quant-ph↗
arXiv2011

Casimir effect from macroscopic quantum electrodynamics

The canonical quantization of macroscopic electromagnetism was recently presented in New J. Phys. 12 (2010) 123008. This theory is here used to derive the Casimir effect, by considering the special case of thermal and zero-point fields. The stress-energy-momentum tensor of the canonical theory follows from Noether's theorem, and its electromagnetic part in thermal equilibrium gives the Casimir energy density and stress tensor. The results hold for arbitrary inhomogeneous magnetodielectrics and are obtained from a rigorous quantization of electromagnetism in dispersive, dissipative media. Continuing doubts about the status of the standard Lifshitz theory as a proper quantum treatment of Casimir forces do not apply to the derivation given here. Moreover, the correct expressions for the Casimir energy density and stress tensor inside media follow automatically from the simple restriction to thermal equilibrium, without the need for complicated thermodynamical or mechanical arguments.

quant-ph↗
arXiv2010

Canonical quantization of macroscopic electromagnetism

Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.

quant-ph↗
arXiv2009

Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.

quant-ph↗
arXiv2009

Casimir-Lifshitz force between moving plates at different temperatures

The zero-temperature Casimir-Lifshitz force between two plates moving parallel to each other at arbitrary constant speed was found in [New J. Phys. 11, 033035 (2009)]. The solution is here generalized to the case where the plates are at different temperatures. The Casimir-Lifshitz force is obtained by calculating the electromagnetic stress tensor, using the method employed by Antezza et al. [Phys. Rev. A 77, 022901 (2008)] for non-moving plates at different temperatures. The perpendicular force on the plates has contributions from the quantum vacuum and from the thermal radiation; both of these contributions are influenced by the motion. In addition to the perpendicular force, thermal radiation from the moving plates gives rise to a lateral component of the Casimir-Lifshitz force, an effect with no quantum-vacuum contribution. The zero-temperature results are reproduced, in particular the non-existence of a quantum-vacuum friction between the plates.

quant-ph↗
arXiv2009

No quantum friction between uniformly moving plates

The Casimir forces between two plates moving parallel to each other are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to "quantum friction" in this case, contrary to previous assertions. The result shows that the Casimir-Polder force on a particle moving at constant speed parallel to a plate also has no lateral component.

quant-ph↗
arXiv2008

An alternative calculation of the Casimir forces between birefringent plates

Barash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn.\ Zaved., Radiofiz., {\bf 12}, 1637 (1978)]. The interesting new feature of the solution compared to the case of isotropic plates is the existence of a Casimir torque which acts to line up the optical axes if they are not parallel or perpendicular. The forces were found from a calculation of the Helmholtz free energy of the electromagnetic field. Given the length of the calculations in this problem and hopes of an experimental measurement of the torque, it is important to check the results for the Casimir forces by a different method. We provide this check by calculating the electromagnetic stress tensor between the plates and showing that the resulting forces are in agreement with those found by Barash.

quant-ph↗
arXiv2007

Quantum levitation by left-handed metamaterials

Left-handed metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two conducting plates may turn from attraction to repulsion if a perfect lens is sandwiched between them. For optical left-handed metamaterials this repulsive force of the quantum vacuum may levitate ultra-thin mirrors.

quant-ph↗
arXiv2003

Supergravity and IOSp(3,1|4) gauge theory

A new formulation of simple D=4 supergravity in terms of the geometry of superspace is presented. The formulation is derived from the gauge theory of the inhomogeneous orthosymplectic group IOSp(3,1|4) on a (4,4)-dimensional base supermanifold by imposing constraints and taking a limit. Both the constraints and the limiting procedure have a clear {\it a priori} physical motivation, arising from the relationship between IOSp(3,1|4) and the super Poincaré group. The construction has similarities with the space-time formulation of Newtonian gravity.

hep-th↗