Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics

A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\hat E$ and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved

Spontaneous emission in a planar Fabry-Perot microcavity

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The spatial routines of daily life in low-income neighbourhoods : escaping the ‘local trap’

In recent years, research and policy have become increasingly interested in the relationship between poverty and place. While research has explored the possibility that living in poor places might make people poorer, policy has been drawn to the idea that poverty and social exclusion have their origins in segregated spaces of the poor and excluded. This paper argues that both perspectives fall into the ‘local trap’ of presuming that people living in areas characterised by economic hardship live spatially bounded, neighbourhood-based lives. Drawing on evidence from interviews with 180 people living in six low-income neighbourhoods across the UK, spatial routines of daily life are revealed to extend regularly beyond the residential neighbourhood through processes of engagement, interaction and exchange. This simple but important finding undermines some key presumptions of contemporary policy and points to the need for improvements in the theoretical models underlying analysis of the relationships between poverty and place

The interaction between poly(ehtylene oxide) and sodium dodecyl sulphate studied by neutron reflection

The composition of the air/solution interface of aqueous mixtures of sodiumdodecyl sulfate (NaDS) and poly-(ethylene oxide) (PEO) has been studied as a function of NaDS concentration and at a fixed concentration of 0.1 wt % PEO using neutron specular reflection. With increasing surfactant concentration, the polymer is progressively displaced from the surface until, at the critical aggregation concentration (CAC), it can no longer be detected (area per segment greater than about 80 Å2. The adsorption of surfactant increases steadily with concentration and shows no sign of a discontinuity at the CAC (4.5 mM at 35°C), which is consistent with the break in the surface tension curve being caused only by the onset of surfactant/polymer aggregation in the bulk solution. At all concentrations the adsorption of NaDS at the air/solution interface is less in the presence of polymer than that in the corresponding solutions without polymer. Nevertheless, it is shown that there is some cooperativity in the adsorption of polymer and surfactant at the interface