Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.

High-pressure adsorption of supercritical gases on activated carbons: An improved approach based on the density functional theory and the bender equation of state

Adsorption of nitrogen, argon, methane, and carbon dioxide on activated carbon Norit R1 over a wide range of pressure (up to 50 MPa) at temperatures from 298 to 343 K (supercritical conditions) is analyzed by means of the density functional theory modified by incorporating the Bender equation of state, which describes the bulk phase properties with very high accuracy. It has allowed us to precisely describe the experimental data of carbon dioxide adsorption slightly above and below its critical temperatures. The pore size distribution (PSD) obtained with supercritical gases at ambient temperatures compares reasonably well with the PSD obtained with subcritical nitrogen at 77 K. Our approach does not require the skeletal density of activated carbon from helium adsorption measurements to calculate excess adsorption. Instead, this density is treated as a fitting parameter, and in all cases its values are found to fall into a very narrow range close to 2000 kg/m(3). It was shown that in the case of high-pressure adsorption of supercritical gases the PSD could be reliably obtained for the range of pore width between 0.6 and 3 run. All wider pores can be reliably characterized only in terms of surface area as their corresponding excess local isotherms are the same over a practical range of pressure.

Experience as a moderator of the media equation: the impact of flattery and praise

This study extends previous media equation research, which showed that the effects of flattery from a computer can produce the same general effects as flattery from humans. Specifically, the study explored the potential moderating effect of experience on the impact of flattery from a computer. One hundred and fifty-eight students from the University of Queensland voluntarily participated in the study. Participants interacted with a computer and were exposed to one of three kinds of feedback: praise (sincere praise), flattery (insincere praise), or control (generic feedback). Questionnaire measures assessing participants' affective state. attitudes and opinions were taken. Participants of high experience, but not low experience, displayed a media equation pattern of results, reacting to flattery from a computer in a manner congruent with peoples' reactions to flattery from other humans. High experience participants tended to believe that the computer spoke the truth, experienced more positive affect as a result of flattery, and judged the computer's performance more favourably. These findings are interpreted in light of previous research and the implications for software design in fields such as entertainment and education are considered. (C) 2004 Elsevier Ltd. All rights reserved.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

A new equation for macroscopic description of capillary rise in porous media

Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case. (C) 2004 Elsevier Inc. All rights reserved.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Projected Gross-Pitaevskii equation for harmonically confined Bose gases at finite temperature

We extend the projected Gross-Pitaevskii equation formalism of Davis [Phys. Rev. Lett. 87, 160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic potentials and outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of the harmonically trapped three-dimensional projected Gross-Pitaevskii equation at finite temperature and consider the dependence of condensate fraction, position, and momentum distributions and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high-energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this nonequilibrium situation.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.