Table of contents

With the help of our referees the journal has grown substantially in recent years. Despite a reject rate of over 50%, we published 40% more pages in 2003 than we did five years ago. Practical considerations mean that we cannot continue to grow at this rate and are now looking to limit the size of the journal. We intend to do this by raising the quality threshold of the journal and rejecting those marginal quality papers which may previously have been accepted.

We are now asking our referees to be particularly strict when judging whether a paper is publishable by rigorously implementing the following criteria. To be acceptable for publication in Journal of Physics A: Mathematical and General:

• papers must make significant, original and correct contributions to one or more topics within the scope of the journal;

• mathematical papers should be clearly motivated by actual or potential application to physical phenomena;

• the length of a paper must be justified by its contents.

We would like to thank all referees for the work they continue to do for us. Effective peer review is essential to the success of the journal and we greatly appreciate the time and effort that referees give up on behalf of the journal. We hope that we can continue this valued collaboration into the future.

For full details of our scope (see also the subject classification) and refereeing requirements please see the journal homepage www.iop.org/Journals/jphysa

We study the mechanism of stochastic resonance for the Landau Ginzburg equation in two space dimensions, perturbed by a white noise. We review how to renormalize the equation in order to avoid ultraviolet divergences. Next, we show that the renormalization amplifies the effect of the small periodic perturbation in the system. We argue that stochastic resonance can be used to highlight the effect of renormalization in a spatially extended system with multiple, stable statistical steady states.

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen.15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin–Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain.

The one-dimensional Ising model is easily generalized to a genuinely nonequilibrium system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetization, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship with a reaction–diffusion model with pair annihilation and creation.

We analyse Haake et al method [1] for coarse graining quantum maps on the sphere from the point of view of realizable physical quantum operations achieved with completely positive superoperators. We conclude that sharp truncations in the style of Haake do not fall into this class.

We formulate the Becker–Döring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and fragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural network (Hopfield) models and show that due to the minimization of the frustration effects the retrieval region of the phase diagram can be significantly enlarged. Moreover, the fraction of misaligned spins is reduced by this effect, and is smaller than that in the infinite connectivity regime. The main cause of this difference is found to be the non-zero fraction of sites with vanishing local field when the connectivity is finite.

A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of hydrodynamic type is characterized.

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for studying the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a basis of quantum SL(n) is obtained by setting the quantum determinant to one. This basis turns out to be equivalent to the dual canonical basis.

The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called 'uncertainty' relation for quite a general class of central potential wells, including the (reduced) Poeschl–Teller and the Gaussian one. It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product P_nl ≡ ⟨r²⟩_nl⟨p²⟩_nl/ℏ², for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Attention is also paid to a number of cases, among the limited existing ones, in which exact analytic or semi-analytic expressions for P_nl can be derived. Finally, numerical results are given and discussed.

Decoherence effect on quantum entanglement of two optical qubits in a lossy cavity interacting with a nonlinear medium (Kerr nonlinearity) is analysed. The qubits are assumed to be initially in the maximally entangled states (Bell or Bell-like states) or the maximally entangled mixed states, on the example of Werner and Werner-like states. Two kinds of measures of the entanglement are considered: the concurrence to describe a decay of the entanglement of formation of the qubits, and the negativity to determine a decay of the entanglement cost under positive-partial-transpose-preserving operations. It is observed that the Kerr nonlinearity, in the discussed decoherence model, does not affect the entanglement of the qubits initially in the Bell or Werner states, although the evolution of the qubits can depend on this nonlinearity explicitly. However, it is shown that for the initial Bell-like state and the corresponding Werner-like state, the loss of the entanglement can be periodically reduced by inserting the Kerr nonlinearity in the lossy cavity. Moreover, the relativity of the entanglement measures is demonstrated, to our knowledge for the first time, as a result of a physical process.

The Bogoliubov procedure in quantum field theory is used to describe a relativistic almost ideal Bose gas at zero temperature. Special attention is given to the study of a vortex. The radius of the vortex in the field description is compared to that obtained in the relativistic fluid approximation. The Kelvin waves are studied and, for long wavelengths, the dispersion relation is obtained by an asymptotic matching method and compared with the non-relativistic result.

Using normal coordinates in a Poincaré–Birkhoff–Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.

We study the onset of buoyancy convection induced in a horizontal layer of a supercritical fluid heated from below. The physical situation, which we investigate, is as follows: the initial fluid temperature is set above the critical temperature. The following two cases are investigated: (a) the bottom surface temperature is raised at time zero and (b) a constant heat flux is given from the bottom surface at time zero. In both cases, the top surface temperature is kept at the initial fluid temperature. First, we analyse the temperature propagations on short time scales. We then investigate the onset conditions of buoyancy convection by linear stability analysis, by which the critical Rayleigh number and the critical wave number are obtained. We finally analyse the delay in the onset of buoyancy convection and the wave number of the convection induced in the supercritical fluid system. We find that power laws apply to the delay and the wave number with respect to the deviation of the initial fluid temperature from the critical temperature. The powers are, in fact, expressed by the critical exponents of some physical properties. This result suggests that the critical exponents can be estimated by measuring the onset times and wave numbers of convection experimentally.

Complex variable hypervirial perturbation theory is applied to the case of oscillator and Coulomb potentials perturbed by a single term potential of the form Vxⁿ or Vrⁿ, respectively. The trial calculations reported show that this approach can produce accurate complex energies for resonant states via a simple and speedy calculation and can also be useful in studies of PT symmetry and tunnelling resonance effects.

The authors would like to correct two inaccuracies. Please see pdf for details.