3D N = 1 SYM Chern-Simons theory on the Lattice

We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term present in this theory. At nonzero Chern-Simons number our implementation suffers from a sign problem which will make the numerical effort grow exponentially with volume. We also show that the theory with vanishing Chern-Simons number is anomalous; its partition function identically vanishes.Comment: v2, minor changes: expanded discussion in section III c, typos corrected, 17 pages, 9 figure

Why beliefs are not dispositional stereotypes

In a series of papers, Schwitzgebel has attempted to revive the dispositionalist account of belief by tweaking it a little and claiming a previously unconsidered advantage over representationalism. The tweaks are to include phenomenal and cognitive responses, in addition to overt behaviour, in the manifestations of a given belief; and to soften the account of dispositions by allowing for dispositional stereotypes. The alleged advantage is that dispositionalism can deal with what Schwitzgebel calls cases of in-between belief, whereas representationalism cannot. In this paper we argue that Schwitzgebel's attempted improvements do not succeed and that, as an account of belief, dispositionalism is seen to be unsatisfactory. The case for this verdict also enables the representationalist position to be enhanced by drawing attention to the diversity of formats in which beliefs are stored

Integrated environmental modelling: achieving the vision

Integrated environmental modelling (IEM) is a recent phenomenon that offers the opportunity to solve complex environmental problems. Whilst it has made great strides in recent years, there are still challenges to be met before IEM is universally accepted and used. This paper describes the current state of IEM and sets out a roadmap for achieving its full potential. A multidisciplinary, multi-agency approach will be required, the main goals of which are to: (1) raise awareness and build confidence in IEM; (2) ensure availability and accessibility of IEM techniques, tools and standards; (3) establish a minimum set of standards; (4) build the IEM skills base; (5) establish an underpinning research and development (R&D) programme; (6) co-ordinate and promote collaboration; and (7) foster IEM use by government, industry and the public. Once these goals have been achieved, then IEM can be deployed to help resolve currently intractable environmental issues, and the IEM methodology can be transferred to other fields

Dual Isomonodromic Deformations and Moment Maps to Loop Algebras

The Hamiltonian structure of the monodromy preserving deformation equations of Jimbo {\it et al } is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras. The nonautonomous Hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on Poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those determining the moment maps. This construction is shown to lead to ``dual'' pairs of matrix differential operators whose monodromy is preserved under the same family of deformations. As illustrative examples, involving discrete and continuous reductions, a higher rank generalization of the Hamiltonian equations governing the correlation functions for an impenetrable Bose gas is obtained, as well as dual pairs of isomonodromy representations for the equations of the Painleve transcendents $P_{V}$ and $P_{VI}$.Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.

Three Dimensional N=2 Supersymmetry on the Lattice

We show how 3-dimensional, N=2 supersymmetric theories, including super QCD with matter fields, can be put on the lattice with existing techniques, in a way which will recover supersymmetry in the small lattice spacing limit. Residual supersymmetry breaking effects are suppressed in the small lattice spacing limit by at least one power of the lattice spacing a.Comment: 21 pages, 2 figures, typo corrected, reference adde

Causes of breakage and disruption in a homogeniser

Many authors have written in the past regarding the exact causes of breakage and disruption in a high pressure homogeniser, but there has been little agreement. This paper investigates some of the most likely causes of the rupture of the walls of unicellular organisms and offers suggestions obtained from various papers and work carried out

Four-Wave mixing in degenerate Fermi gases: Beyond the undepleted pump approximation

We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to a decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case four-wave mixing can persist for much longer times compared to the case of negligible back-action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.Comment: 9 pages, 8 figure

Semiclassical force for electroweak baryogenesis: three-dimensional derivation

We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constant h-bar. We show that to first order in h-bar the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with the 1+1-dimensional case studied in a former paper. We find that an identical semiclassical force can be obtained by the WKB method. Applications to the MSSM are also mentioned.Comment: 19 page

Dynamics of Fermionic Four-Wave Mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the novel technique of ``atom echoes''.Comment: 8 pages, 7 figure