Table of contents

The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterizing the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincaré or Galilei) by making some subgroup local. The corresponding dynamics is generated by a vector field inside the kernel of a pre-symplectic form which is derived from the canonical left-invariant 1-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inönü–Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to, in principle, testable predictions.

The kinetic energy density t_G(r), where G denotes the gradient form (∇ψ)², is known to be a functional of the ground-state density ρ(r), but the functional remains unknown. For an arbitrary number of closed shells in a bare Coulomb field, an exact first-order differential equation is derived giving t_G(r) solely in terms of s-state information. Numerical illustrations are given of the main analytical results.

In this letter, we use the method of constructing exact solutions on lattices proposed by Kinnersley and described in Schmidt (1979 Phys. Rev. B 20 4397), to obtain exact compacton solutions in discrete models. We examine the linear stability of such solutions, both for the bright compacton and for the dark compacton cases. We focus on a 'quantization condition' that the width of the profile should satisfy. We also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings. Our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus. The possibility of multi-compacton solutions is considered.

We present explicit forms of discrete Painlevé equations in which the independent variable and the parameter enter through the arguments of elliptic functions. These equations have eight degrees of freedom and the geometry of their transformations is described by the affine Weyl group E⁽¹⁾₈.

We discuss one-dimensional stochastic processes defined through the Temperley–Lieb algebra related to the Q = 1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics.

The geometric amplitude factor in an over-damped LCR circuit with time-dependent inductance, capacitance and resistance is obtained. A simple scheme to measure this factor is also proposed.

We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a by-product, we obtain evidence in favour of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favour of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.

We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The resulting distributions exhibit an unusual finite-size scaling behaviour and they are also sensitive to the initial conditions. We argue that fluctuations in the number of nodes of degree k become Gaussian for fixed degree as the size of the network diverges. We also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution.

Single-particle motion and self-diffusion in a two-dimensional dusty plasma are investigated by molecular dynamic simulation. The velocity autocorrelation function indicates that the single-particle motion is strongly coupled to the collective motion in the dusty plasma when the coupling parameter is high enough. The point defects play an important role in the particle self-diffusion process. A simple point defect motion model is developed to explain the mechanism of self-diffusion and estimate the self-diffusion coefficient in the dusty plasma. The value of the self-diffusion coefficient calculated by using the model is in agreement with the result obtained from mean square displacement for a two-dimensional dusty plasma crystal.

Identities and inequalities are proved for the order parameters, correlation functions and their derivatives of the Ising spin glass. The results serve as additional evidence that the ferromagnetic phase is composed of two regions, one with strong ferromagnetic ordering and the other with the effects of disorder dominant. The Nishimori line marks a crossover between these two regions.

We present two kinds of integral solutions to the quantum Knizhnik–Zamolodchikov equations for the 2n-point correlation functions of the Heisenberg XYZ antiferromagnet. Our first integral solution can be obtained from those for the cyclic SOS model by using the vertex–face correspondence. By the construction, the sum with respect to the local height variables k₀, k₁, ..., k_2n of the cyclic SOS model remains other than the n-fold integral in the first solution. In order to perform these summations, we improve this to find the second integral solution of (r + 1)n-fold integral for r ∊ _>1, where r is a parameter of the XYZ model. Furthermore, we discuss the relations among our formula, Lashkevich–Pugai's formula and that of Shiraishi.

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: the magnetic length l_B, the Bohr radius l₀, and the radius of the sphere R. The energy spectrum of the particle is found by solving a Schrödinger equation of the Heun type, using the technique of continued fractions. This displays a rich set of functioning regimes where ratios R/l_B and R/l₀ take definite values.

We study the nature of electronic states in one-dimensional continuous models with weak correlated disorder. Using a perturbative approach, we compute the inverse localization length (Lyapunov exponent) up to terms proportional to the fourth power of the potential; this makes it possible to analyse the delocalization transition which takes place when the disorder exhibits specific long-range correlations. We find that the transition consists of a change of the Lyapunov exponent, which switches from a quadratic to a quartic depending on the strength of the disorder. Within the framework of the fourth-order approximation we also discuss the different localization properties which distinguish Gaussian from non-Gaussian random potentials.

The exact particle and energy densities for a noninteracting Fermi gas at any temperature in a d-dimensional harmonic trap are obtained, and they are expressed by the gamma function and the Laguerre polynomials. The obtained analytical expressions are rapidly converging series and may be conveniently used for the numerical calculations. These expressions can be used for the comparison with the experimental results and for the test of the local density approximation.

A method based on the Padé approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Padé approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Padé approximations. Results are presented for several cases of Padé approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases.

A noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Following Gurevich and Saponov (2001 J. Phys. A: Math. Gen.34 4533–69) and using the Cayley–Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a multiplicative structure in their family. Also, we compute a pairing between quantum line bundles and finite-dimensional representations of the NC sphere in the spirit of the NC index theorem. Moreover, we introduce projective modules being NC counterparts of tangent vector bundles and those of differential forms and define an analogue of the de Rham complex making use of these modules.

We consider the linear stability of a cylindrical rotating jet of pure superfluid held together by surface tension. A necessary and sufficient condition for stability to axisymmetric disturbances is derived which corresponds to that of a classical inviscid fluid. For axisymmetric disturbances we find that the vortex tension does not affect the range of unstable axial wave numbers, only the temporal growth rate and the most critical wave number. A sufficient condition for the stability of a general disturbance is derived which corresponds to that of a classical inviscid fluid. We find for non-axisymmetric disturbances, that the vortex tension increases the range of unstable wave numbers. The temporal growth rates of the unstable azimuthal modes increase with vortex tension.

An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann–Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators.

We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing centre-of-mass vector → , which corresponds to the strong magnetic field limit, occurring for example in the fractional quantum Hall effect. Using the solutions of the biconfluent Heun equation, we compute the eigenstates and show that there are two sets of solutions. The first one corresponds to a system of three independent anyons which have their angular momenta fixed by the value of the magnetic field and specified by a dimensionless parameter C ≃ l_B/l₀, the ratio of l_B, the magnetic length, over l₀, the Bohr radius. This anyonic character, consistent with quantum mechanics of identical particles in two dimensions, is induced by competing physical forces. The second one corresponds to the case of the Landau problem when C → 0. Finally we compare these states with the quantum Hall states and find that the Laughlin wavefunctions are special cases of our solutions under certain conditions.

The present work concerns the study of the convergence properties of the nonlinear S transformation. A fast and accurate numerical evaluation of highly oscillatory semi-infinite integrals involved in the analytic expressions of molecular integrals over Slater-type orbitals is obtained using the S transformation. These semi-infinite integrals involve spherical and reduced Bessel functions. The convergence properties are analysed and they show that the approximations obtained using the S approach converge to the exact values of the semi-infinite integrals without any constraint. The numerical tables show that the S method gives unprecedented accuracy with speed-up by a factor 2 over the H method and a factor 10 over the transformation. This illustrates the superiority of this new approach.

This practical example of angle holonomy has a mis-stated derivation which is rectified here lest it discredit the results obtained, which need no amendment.

Corrections to J A Gracey 1991 J. Phys. A: Math. Gen.24 L197-L200.

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With effect from 1 January 2003 (volume 36), the following classification scheme will be introduced for research papers published in Journal of Physics A: Mathematical and General. We believe that this new scheme will help to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work.

We also list below some more detailed subject areas which should help define each section heading. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. Whenever possible, we will respect the author's wishes on placement and undertake to inform authors when we feel that a different classification is more appropriate.

We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org).

1. Statistical physics May include papers on

• statistical mechanics, lattice theory and thermodynamics

• quantum statistical mechanics and Bose-Einstein condensation

• phase transitions and critical phenomena

• numerical and computational methods

• theories of interacting particles (many-body theories)

• theoretical condensed matter and mesoscopic systems

• disordered systems, spin glasses and neural networks

• nonequilibrium processes

2. Chaotic and complex systems May include papers on

• nonlinear dynamics and classical chaos

• quantum chaos

• cellular automata

• biophysics

3. Mathematical physics May include papers on

• integrable systems

• random matrix theory

• special functions

• Lie algebras and quantum groups

• classical mechanics

• inverse problems

4. Quantum mechanics and quantum information theory May include papers on

• foundations of quantum mechanics

• quantum information, computation and cryptography

• theoretical quantum optics

• open quantum systems

5. Classical and quantum field theory May include papers on

• gauge and conformal field theory

• quantum electrodynamics and quantum chromodynamics

• string theory and its developments

• classical electromagnetism

6. Theory of continuous media May include papers on

• fluid dynamics and turbulence

• plasma physics