Scattering theory of cooling and heating in optomechanical systems

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Computational techniques for a simple theory of conditional preferences

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences.

'Trusting the numbers': mineral prospecting, raising finance and the governance of knowledge

Mineral prospecting and raising finance for ‘junior’ mining firms has historically been regarded as a speculative activity. For the regulators of securities markets upon which ‘junior’ mining companies seek to raise capital, a perennial problem has been handling not only the indeterminacy of scientific claims, but also the social basis of epistemic practices. This paper examines the production of a system of public warrant and associated knowledge practices intended to enable investors to differentiate between ‘destructive’ and ‘productive’ varieties of financial speculation. It traces the use of the notion of ‘disclosure’ in constructing and legitimizing the ‘juniors’ market in Canada. It argues that though the work of ‘economics’ may be necessary in the construction of markets, it is by no means sufficient. Attention must also be given to the ways in which legal models of ‘the free-market’ can be translated and constantly re-worked across the sites and spaces of regulatory practice, animating the geographies of markets.

K-Theory of Azumaya Algebras over Schemes

Let X be a connected, noetherian scheme and A{script} be a sheaf of Azumaya algebras on X, which is a locally free O{script}-module of rank a. We show that the kernel and cokernel of K(X) ? K(A{script}) are torsion groups with exponent a for some m and any i = 0, when X is regular or X is of dimension d with an ample sheaf (in this case m = d + 1). As a consequence, K(X, Z/m) ? K(A{script}, Z/m), for any m relatively prime to a. © 2013 Copyright Taylor and Francis Group, LLC.