Table of contents

For 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 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

• nonlinear dynamics and classical chaos

• quantum chaos

• cellular automata

• biophysics

• integrable systems

• random matrix theory

• special functions

• Lie algebras and quantum groups

• classical mechanics

• inverse problems

• foundations of quantum mechanics

• quantum information, computation and cryptography

• theoretical quantum optics

• open quantum systems

• gauge and conformal field theory

• quantum electrodynamics and quantum chromodynamics

• string theory and its developments

• classical electromagnetism

• fluid dynamics and turbulence

• plasma physics

This section of the journal publishes high quality short reports of important new results. Letters are both timely and important enough to merit rapid publication; they should not be more than 3500 words (6 journal pages) in length. The publication process of Letters is accelerated by using streamlined refereeing and production procedures. Accepted Letters benefit from higher visibility through being available free of charge on the journal web page to non-subscribers.

Letters will normally be assessed by one senior referee, usually a board member, using the following criteria. To be accepted for publication, a Letter to the Editor should:

(i) present important new results (ii) be likely to stimulate further research (iii) be of interest to the wider mathematical or statistical physics community (iv) be sufficiently significant to justify accelerated publication.

Serial publication of letters - where research is published as a series of letters rather than as full research papers - is not acceptable in the journal.

Letters that do not fit the above criteria may be considered as Research Papers depending on the referee's recommendation. There is no lower limit on the length of papers but they should contain important new results.

Comments on Letters published are invited. These should be no longer than two journal pages in length and (if accepted) will be published at the end of the section together with their corresponding Reply if appropriate. Replies are limited to one journal page in length.

For details on how to submit, please see our brief guide for authors on the inside front cover of the journal or the information for authors page on our web site (www.iop.org/Journals/asi).

The decay of directional correlations in self-avoiding random walks on the square lattice is investigated. Analysis of exact enumerations and Monte Carlo data suggest that the correlation between the directions of the first step and the jth step of the walk decays faster than j⁻¹, indicating that the persistence length of the walk is finite.

It is known that if an equation describes non-trivial one-parameter families of pseudo-spherical surfaces, its conservation laws, (generalized, nonlocal) symmetries and Bäcklund transformations can be studied by geometrical means [4, 10]. In this letter it is pointed out that there exist correspondences, or 'generalized Bäcklund transformations', between arbitrary solutions (satisfying some genericity conditions) of any two single equations describing pseudo-spherical surfaces. Then, the notion of a hierarchy of equations of pseudo-spherical type is introduced, and a theorem stating that there also exist correspondences between arbitrary solutions of any two such hierarchies is presented. A full account of these results appears elsewhere [12, 13].

In this letter, we analyse two bidirectional sixth-order partial differential equations, which are reductions in (1 + 1) dimensions of equations belonging to the KP hierarchy. They have fourth-order and fifth-order Lax pairs, respectively. We derive their Bäcklund transformations and, from the nonlinear superposition formula, we can build their soliton solutions like a Grammian. The interesting dynamics of these solitons is that they may describe not only the overtaking collision but also the head-on collision of solitary waves of different type and shape.

We use a geometrical formalism of Galilean invariance to build various hydrodynamics models. It consists in embedding the Newtonian spacetime into a non-Euclidean 4 + 1 space and provides thereby a procedure that unifies models otherwise apparently unrelated. After expressing the Navier–Stokes equation within this framework, we show that slight modifications of its Lagrangian allow us to recover the Chaplygin equation of state as well as models of superfluids for liquid helium (with both its irrotational and rotational components). Other fluid equations are also expressed in a covariant form.

The steady-state currents and densities of a one-dimensional totally asymmetric exclusion process (TASEP) with particles that occlude an integer number (d) of lattice sites are computed using various mean-field approximations and Monte Carlo simulations. TASEPs featuring particles of arbitrary size are relevant for modelling systems such as mRNA translation, vesicle locomotion along microtubules and protein sliding along DNA. We conjecture that the nonequilibrium steady-state properties separate into low-density, high-density, and maximal current phases similar to those of the standard (d = 1) TASEP. A simple mean-field approximation for steady-state particle currents and densities is found to be inaccurate. However, we find local equilibrium particle distributions derived from a discrete Tonks gas partition function yield apparently exact currents within the maximal current phase. For the boundary-limited phases, the equilibrium Tonks gas distribution cannot be used to predict currents, phase boundaries, or the order of the phase transitions. However, we employ a refined mean-field approach to find apparently exact expressions for the steady-state currents, boundary densities, and phase diagrams of the d ≥ 1 TASEP. Extensive Monte Carlo simulations are performed to support our analytic, mean-field results.

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction–diffusion systems, namely the Fisher equation and the time-dependent Ginzburg–Landau equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction–diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution.

We present a general procedure for finding recurrence relations of the radial wavefunctions for Nth-dimensional isotropic harmonic oscillators and hydrogenlike atoms.

An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schrödinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.

The Δ ≠ 1 generalization of the q-symmetrized Harper equation is discussed in terms of wavefunctions expressed by Laurent series. Proceeding by recursion leads to a nontrivial Δ-dependent generalization of the characteristic energy polynomial, with a special emphasis on a continuous dependence on the commensurability parameter. The multiplicity parameter which is responsible for the amount of coprime realizations of the commensurability parameter is also accounted for. The present energies have been derived so as to reproduce particular ones obtained before as limiting cases.

Hyperbolic Kac–Moody superalgebras are classified in terms of their Dynkin diagrams. These types of Kac–Moody superalgebras are those whose diagrams revert to either that of simple or affine superalgebras upon deletion of one of the vertices. It is found that the maximum rank of this type of algebra is 6.

This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation

To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math.3 201–30), give the formula of the corresponding viscosity solutions by Hopf–Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.

In this paper, we generalize the Jaynes–Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation.

The typical avoided crossings for Hermitian quantum systems depending on parameters, the diabolic crossing scenario, are generalized to the non-Hermitian case, e.g. for resonances. Two types of crossings appear: for type I, the real parts show an avoided and the imaginary parts a true crossing of the eigenenergies, and for type II the opposite is found. A simple symmetric non-Hermitian two-state matrix Hamiltonian is analysed in detail. The diabolic point bifurcates into two exceptional ones on exceptional lines where the matrices are defective. The adiabatic transport of eigenvectors and eigenstates in parameter space is discussed in this generalized diabolic crossing scenario, in particular the geometric Berry phases for a cyclic variation of system parameters, depending on the topology of the closed curves with respect to the exceptional lines.

The complex energy resonances of a double δ potential well in a constant (Stark) field are studied. Varying the two system parameters (well distance and field strength) we investigate the behaviour of the resonance energies and wavefunctions both analytically and numerically. Different crossing scenarios for the real and imaginary parts of two resonance energies are observed and compared with a simple two-state model. In addition, a point in parameter space where both the real and imaginary parts of the two energies degenerate, an exceptional point, is found. Varying the system parameters around this exceptional point, the behaviour of energies and wavefunctions is discussed and the corresponding geometric phases, or Berry phases, for this non-Hermitian system are considered.

For a quantum-mechanical counting process we show ergodicity, under the condition that the underlying open quantum system approaches equilibrium in the time mean. This implies equality of time average and ensemble average for correlation functions of the detection current to all orders and with probability 1.

It is well known that the analysis of a relativistic n-body problem invariant under the transformations of the Poincaré group and involving only one time has only been done for n = 1. For n > 1 one uses the second quantization formalism of field theory. In this paper we state it in the ordinary space time coordinates associated with the n-bodies as Dirac did in the one body case. We apply the formalism first to the two-body problem and have a development of the Hamiltonian in terms of powers of (1/c²), that allows us to determine the spectra of bottomonium and compare with the experimental results.

We present an open-loop (bang-bang) scheme to control decoherence in a generic one-qubit quantum gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.

A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A method for constructing regularizers in the new sense is proposed and justified.

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieliński (2002 J. Phys. A:Math. Gen.35 1405) is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (URs) on a circle are those based on the Gram–Robertson matrix. Several of these generalized URs are displayed and related criteria for squeezed states are discussed.