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 is a call for contributions to a Special Issue ofJournal of Physics A: Mathematical and General entitled `Statistical Physics of Disordered Systems: from Real Materials to Optimization and Codes'. This issue should be a place for high quality original work. We stress the fact that we are interested in having the topic interpreted broadly: we would like to have contributions ranging from equilibrium and dynamical studies of spin glasses, glassy behaviour in amorphous materials, and low temperature physics, to applications in non-conventional areas such as error correcting codes, image analysis and reconstruction, optimization, and algorithms based on statistical mechanical ideas. We believe that we have arrived at a very exciting moment for the development of this multidisciplinary approach, and that this issue will be of a high standard and prove to be a very useful tool in the future.

The Editorial Board has invited E Marinari, H Nishimori and F Ricci-Tersenghi to serve as Guest Editors for the Special Issue. Their criteria for acceptance of contributions are the following:

• The subject of the paper should relate to the statistical physics of disordered systems.

• Contributions will be refereed and processed according to the usual procedures of the journal.

• Papers should be original (they should not be simply reviews of authors' own work that is already published elsewhere).

• Review articles will be considered for inclusion in the Special Issue only in very special cases. The editors will analyse potential proposals of reviews, and if needed they will ask for some review contributions.

The guidelines for the preparation of contributions are the following:

•The deadline for submission of contributions has now been extended to 1 May 2003. This deadline will allow the Special Issue to appear in about November 2003.

• There is a nominal page limit of 15 printed pages (approximately 9000 words) per research contribution. The contributions that have been approved by the Guest Editors as review articles will have a limit of 30 printed pages (18000 words). Papers exceeding these limits may be accepted at the discretion of the Guest Editors. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa.

• Contributions to the Special Issue should if possible be submitted electronically at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'. Submissions should ideally be in either standard LaTeX form or Microsoft Word. Please see the web site for further information on electronic submissions.

• Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'.

• All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address.

This Special Issue will be published in both paper and online editions of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue in addition to the usual 25 free offprints of their article.

E Marinari, H Nishimori and F Ricci-Tersenghi

Guest Editors

It is shown that the Lindblad equation accounts for memory effects. That is to say, Lindblad operators can be constructed in a natural manner such that a memory term appears in the asymptotic (time → ∞) region; at the same time the expectation values depend on the initial state. Furthermore, a procedure for extending the Lindblad equation to an equation of motion for an ideal Bose 'gas' of 'particles', i.e. systems with non-trivial internal structure, is described. Initially in some quantum state this collection of 'particles' will asymptotically turn into an equilibrium ensemble whose probability distribution is determined by the Lindblad operators building the dissipative part of the equation of motion.

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al (2002 Phys. Rev. Lett.88 114101) and by Bogomolny and Schmit (2002 Phys. Rev. Lett.88 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps.

We study opinion formation in a population of leftists, centrists and rightist. In an interaction between neighbouring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist), while leftists and rightists do not affect each other. The evolution is controlled by the initial density of centrists ρ₀. For any spatial dimension the system reaches a centrist consensus with probability ρ₀, while with probability 1 − ρ₀ the final state is either an extremist consensus, or a frozen population of leftists and rightists. In one dimension, we determine the opinion evolution by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. The approach to the final state is governed by a t^−ψ long-time tail, with ψ → 2ρ₀/π as ρ₀ → 0. In the one-dimensional frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x^−2(1−ψ) and the average domain length is L^2ψ, where L is the length of the system.

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with various boundary conditions (BC). Using conformal mappings we deduce the exponent η_σ(T) of the order parameter correlation function and its surface analogue η_∥(T) as a function of the temperature in the critical (low-temperature) phase of the model. The temperature dependence of both exponents is obtained numerically with a good accuracy up to the Kosterlitz–Thouless transition temperature. The bulk exponent follows from simulations of correlation functions with periodic boundary conditions or order parameter profiles with open boundary conditions and with symmetry breaking surface fields. At very low temperatures, η_σ(T) is found in pretty good agreement with the linear temperature-dependence of Berezinskii's spin-wave approximation. We also show some evidence that there are no noticeable logarithmic corrections to the behaviour of the order parameter density profile at the Kosterlitz–Thouless (KT) transition temperature, while these corrections exist for the correlation function. At the KT transition the value η_σ(T_KT) = 1/4 is accurately recovered. The exponent associated with the surface correlations is similarly obtained after a slight modification of the boundary conditions: the correlation function is computed with free BC, and the profile with mixed fixed–free BC. It exhibits a monotonic behaviour with temperature, starting linearly according to the spin-wave approximation and increasing up to a value η_∥(T_KT) ≃ 1/2 at the Kosterlitz–Thouless transition temperature. The thermal exponent η_ε(T) is also computed and we give some evidence that it keeps a constant value in agreement with the marginality condition of the temperature field below the KT transition.

We consider a generalization of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalization group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t. For d > 2, this is constant, but for d < 2 it decays as a power t^−α, which we compute to (ε²) in an expansion in ε = 2 − d. The second-order term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)⁻ and compute exactly.

Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p_Γ of the underlying microscopic phase space trajectories Γ over a time interval of length τ satisfies p_Γ ∝ exp(τσ_Γ/2k_B) where σ_Γ is the time-averaged rate of entropy production of Γ. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as τ → ∞; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary, non-equilibrium systems. In turn, the accumulating empirical evidence for these results lends support to Jaynes' formalism as a common predictive framework for equilibrium and non-equilibrium statistical mechanics.

This paper is concerned with a lattice model which is suited to square–rectangle transformations characterized by two strain components. The microscopic model involves nonlinear and competing interactions, which play a key role in the stability of soliton solutions and emerge from interactions as a function of particle pairs and noncentral type or bending forces. Special attention is devoted to the continuum approximation of the two-dimensional discrete system with the view of including the leading discreteness effects at the continuum description. The long-time evolution of the localized structures is governed by an asymptotic integrable equation of the Kadomtsev–Petviashvili I type which allows the explicit construction of moving multi-solitons on the lattice. Numerical simulation performed at the discrete system investigates the stability and dynamics of the multi-soliton in the lattice space.

An upper bound is derived for the exact ground-state energy in 2D, E_N ≤ −(me⁴/2ℏ²)(N^3/2/50π²), of 'bosonic matter' consisting of N positive and N negative charges with Coulombic interactions. This is to be compared with the classic N^7/5 3D-law of Dyson and gives rise to a more 'violent' collapse of such matter in 2D for large N. The derivation is based on a rigorous analysis which, in the process, controls the negative part of the Hamiltonian over its positive kinetic energy part and detailed estimates needed for counting trial wavefunctions of arbitrary states. A formal dimensional analysis in the style of Dyson alone shows, in arbitrary dimensions of space d = 1, 2, ..., that E_N ≃ −(me⁴/2ℏ²)C_dN^ρ, ρ = (d + 4)/(d + 2), where C_d is a positive constant depending on d, consistent with our rigorous bound, and we are led to conjecture that 'bosonic matter' is unstable in all dimensions.

We study analytically and numerically the role of temperature shifts in the simplest model where the energy landscape is explicitly hierarchical, namely the Sinai model. This model has both attractive features (there are valleys within valleys in a strict self-similar sense), but also one important drawback: there is no phase transition so that the model is, in the large-size limit, effectively at zero temperature. We compute various static chaos indicators, that are found to be trivial in the large-size limit, but exhibit interesting features for finite sizes. Correspondingly, for finite times, some interesting rejuvenation effects, related to the self-similar nature of the potential, are observed. Still, the separation of time scales/length scales with temperature in this model is much weaker than in experimental spin glasses.

We have extended the entropic sampling Monte Carlo method to the case of path integral representation of a quantum system. A two-dimensional density of states is introduced into path integral form of the quantum canonical partition function. Entropic sampling technique within the algorithm suggested recently by Wang and Landau (Wang F and Landau D P 2001 Phys. Rev. Lett.86 2050) is then applied to calculate the corresponding entropy distribution. A three-dimensional quantum oscillator is considered as an example. Canonical distributions for a wide range of temperatures are obtained in a single simulation run, and exact data for the energy are reproduced.

This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction.

The averages of ratios of characteristic polynomials det(λ − X) of N × N random matrices X are investigated in the large-N limit for the GUE, GOE and GSE ensembles. The density of states and the two-point correlation function are derived from these ratios. The method relies on an extension of the Harish-Chandra, Itzykson, Zuber integrals to the GOE ensemble and to supergroups, which are explicitly computed through heat kernel differential equations. An external matrix source, linearly coupled to the random matrices, may also be added to the Gaussian distribution, and allows for a discussion of the universality of the GOE results in the large-N limit.

Approximate Lie symmetries of the (2 + 1)-dimensional nonlinear diffusion equation with a small convection are completely classified. It is known that the invariance principle furnishes a systematic method of solving initial-value problems. The solutions of instantaneous source type of the 2D diffusion–convection equation are obtained for the case of power-law diffusivity, using a symmetry reduction.

For the general linear second-order q-difference equation, we show the interconnection between the factorization method and the Laguerre–Hahn polynomials on the general q-lattice. Applications are then given in the cases of the hypergeometric and Askey–Wilson second-order q-difference equations.

The involutive automorphisms of hyperbolic Kac–Moody superalgebras are computed from the Satake superdiagrams corresponding to these algebras. These are then used to furnish a general treatment of the Iwasawa decomposition of these algebras. In particular, we consider ⁽¹⁾(2, 1, α) and Â⁽¹⁾(0, 1) as representative examples for the purpose of illustration.

Geometric and algebraic aspects of multi-ratios M_2N are investigated in detail. Connections with Menelaus' theorem, Clifford configurations and Maxwell's reciprocal quadrangles are utilized to associate the multi-ratios M₄, M₈ and M₈ with tetrahedra, octahedra and cubo-octahedra respectively. Integrable maps defined on face-centred (fcc) lattices and irregular lattices composed of the face centres of simple cubic lattices are constructed and related to the discrete KP and BKP equations and the integrable discrete Darboux system governing conjugate lattices. An interpretation in terms of integrable irregular lattices of slopes on the plane is also given.

The matrix exponential plays an important role in solving systems of linear differential equations. We will give a general expansion of the matrix exponential S = exp[λ(A + B)] as S_n,m = e^λb_nδ_n,m + ∑_{q = 1}^∞ ∑_{l1 = 0}^N ⋯ ∑_{lq−1 = 0}^Na_n,l1 ⋯ a_lq−1,mC^(q)_{n,l1,...,lq−1,m}(B, λ) with C^(q)_{n,l1,...,lq−1,m}(B, λ) being an analytical expression in b_n, b_l1, b_l2, ... b_lq−1, b_m, and the scalar coefficient λ. A is a general N × N matrix with elements a_n,m and B a diagonal matrix with elements b_n,m = b_nδ_n,m along its diagonal. The convergence of this expansion is shown to be superior to the Taylor expansion in terms of (λ[A + B]), especially if elements of B are larger than the elements of A. The convergence and possibility of solving the phase problem through multiple scattering is demonstrated by using this expansion for the computation of large-angle convergent beam electron diffraction pattern intensities.

A direct approach is applied to the periodic amplification of a soliton in an optical fibre link with loss. In a single soliton case, the adiabatic solution and first-order correction are given for the system. The apparent advantage of this direct approach is that it not only presents the slow evolution of soliton parameters, but also the perturbation-induced radiation, and can be easily used to investigate the system of dispersion management with periodically varying dispersion and other fields.

Based on the non-autonomous quantum master equation, we investigate the dissipative and decoherence properties of the two-level atom system interacting with the environment of thermal quantum radiation fields. For this system, by a novel algebraic dynamic method, the dynamical symmetry of the system is found, the quantum master equation is converted into a Schrödinger-like equation and the non-Hermitian rate (quantum Liouville) operator of the master equation is expressed as a linear function of the dynamical u(2) generators. Furthermore, the integrability of the non-autonomous master equation has been proved for the first time. Based on the time-dependent analytical solutions, the asymptotic behaviour of the solution has been examined and the approach to the equilibrium state has been proved. Finally, we have studied the decoherence property of the multiple two-level atom system coupled to the thermal radiation fields, which are related to the quantum register.

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy expended in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions, determine the fields for a general one-qubit gate, and use the Y gate as an example. We argue that in the case of less than three controls, only the physical intuition does not provide a straight reasonable solution, and solve the problem in the case of a unique control minimizing the energy consumption.

Two-dimensional free surface potential flow issued from an opening of a container is considered. The flow is assumed to be inviscid and incompressible. The mathematical problem, which is characterized by the nonlinear boundary condition on the free surface of an unknown equation, is solved via a series truncation. We computed solutions for all Weber numbers. Our problem is an extension of the work done by Ackerberg and Liu (1987 Phys. Fluids30 289–96), the results confirm and extend their results.

We study fluid flow and the formation of viscous fingering patterns on a two-dimensional conical background space, defined as the conical Hele–Shaw cell. We approach the problem geometrically and study how the nontrivial topological structure of the conical cell affects the evolution of the interface separating two viscous fluids. We perform a perturbative weakly nonlinear analysis of the problem and derive a mode-coupling differential equation which describes fluid–fluid interface behaviour. Our nonlinear study predicts the formation of fingering structures in which fingers of different lengths compete and split at their tips. The shape of the emerging patterns show a significant sensitivity to variations in the cell's topological features, which can be monitored by changing the cone opening angle. We find that for increasingly larger values of the opening angle, finger competition is inhibited while finger tip-splitting is enhanced.