Table of contents

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 is 31 March 2003. This deadline will allow the Special Issue to appear in about October 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

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

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

We consider quantum systems composed of N qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if an N-qubit state ρ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.

Representation bases of unitary parasupersymmetry algebra of arbitrary order p is constructed by some one-dimensional models which are shape invariant with respect to the main quantum number n. Consequently, the isospectral Hamiltonians and their exact solutions are obtained as labelled by the main quantum number n.

We derive the RG flow equations of the sliding Luttinger liquid perturbed by charge-density-wave (CDW) and superconducting (SC) operators. Using them we study the phase diagram of an array of XXZ spin chains coupled by Ising terms. In the weak-coupling regime we find a new class of self-dual and antiself-dual unstable fixed points.

The thermodynamic and retrieval properties of fully connected Blume–Emery–Griffiths networks are studied using replica mean-field theory. These networks can be considered as generalizations of the Hopfield model to the storage of ternary patterns. Capacity–temperature phase diagrams are derived for several values of the pattern activity. It is found that the retrieval phase is the largest in comparison with other three-state neuron models. Furthermore, the meaning and stability of the so-called quadrupolar phase is discussed as a function of both the temperature and the pattern activity. Where appropriate, the results are compared with the diluted version of the model.

We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non-constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activated processes. We formulate a mean-field version of the models, which keeps most of the features of the finite dimensional ones, and solve analytically the out-of-equilibrium dynamics in the low temperature regime where activation plays an essential role.

The thermodynamic Bethe ansatz method is employed for the study of the integrable critical RSOS(q₁, q₂; q) model. The high and low temperature behaviours are investigated, and the central charge of the effective conformal field theory is derived. The obtained central charge is expressed as the sum of the central charges of two generalized coset models.

Single-species reaction–diffusion systems on a one-dimensional lattice are considered, in which more than two neighbouring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E_n(t), the probability that n consecutive sites are empty at time t. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbour interaction is studied.

Two different types of integrable impurities in a spin ladder system are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly with the Bethe ansatz equations as well as the energy eigenvalues obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. In one of the models the spin gap decreases by increasing the impurity strength Λ. Moreover, for a fixed Λ, a reduction in the spin gap by increasing the impurity concentration is also observed.

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise, and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion, and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in two-dimensional flows that show chaotic advection are proposed.

This paper presents a new cellular automata model for describing synchronized traffic flow. The fundamental diagrams, the spacetime plots and the 1 min average data have been analysed in detail. It is shown that the model can describe the outflow from the jams, the light synchronized flow as well as heavy synchronized flow with average speed greater than approximately 24 km h⁻¹. As for the synchronized flow with speed lower than 24 km h⁻¹, it is unstable and will evolve into the coexistence of jams, free flow and light synchronized flow. This is consistent with the empirical findings (Kerner B S 1998 Phys. Rev. Lett.81 3797).

Electrokinetic phenomena in porous media are studied by application of the effective medium theory and the theory of duality transformation. We deduce new exact relations and analytical formulae for the effective constants of the macroscopic tensor. We also prove that the effective tensors obtained by these approaches coincide for 2D problems. The obtained results for the electrokinetic processes are closely related to similar results derived for piezoelectric composites because of a common mathematical background.

We present a complete description of the classical (Lie) symmetries of a coupled system of partial differential equations comprising a pair of semilinear reaction–diffusion equations with constant diffusivities and arbitrary nonlinearities in the reaction terms, in any number of spatial dimensions. Part I (Cherniha R M and King J R 2000 J. Phys. A: Math. Gen.33 267–82, J. Phys. A: Math. Gen.33 7839–41) addressed the case of unequal diffusivities; here we complete the analysis by treating the case of equal diffusivities in which the symmetry structure is richer still. Such models arise in the description of numerous physical, chemical and biological systems and we also indicate the possible application in such contexts of some of the specific cases arising from the group classification. Specifically, a variety of Lie's ansätze and exact solutions of the so-called λ − ω reaction–diffusion systems, of a type that arises in mathematical biology, are constructed.

The automorphisms of all four-dimensional, real Lie algebras are presented in a comprehensive way. Their action on the space of 4 × 4, real, symmetric and positive definite matrices defines equivalence classes which are used for the invariant characterization of the four-dimensional homogeneous spaces which possess an invariant basis.

We study the Schrödinger operator −Δ − αδ(x − Γ) in L²(³) with a δ interaction supported by an infinite non-planar surface Γ which is smooth and admits a global normal parametrization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large, this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a 'two-dimensional' comparison operator determined by the geometry of the surface Γ.

A complete set of invariants for three states in the quantum space of states is obtained together with a complete set of relationships linking them. This is done in a way that preserves the self-duality of and leads to a clear geometric description of invariants (distances, lateral phases; Hermitian angles, angular phases; and two purely triangular phases). Some of these invariants appear here for the first time. Symplectic area (and hence the triangle geometric phase) is proportional to a 'mixed phase excess', thus extending to the relation 'area-angular excess' in the real sphere. The new triangle lateral phases provide a description, intrinsic to , of relative phases in a superposition. This approach also provides closed expressions for the triangle holonomy associated with the usual Fubini–Study metric in , as well as many other expressions for similar 'loop' operators along the triangle, including closed and exact expressions for the triangle Aharonov–Anandan geometric phase.

Perturbation expansions up to third order for the generalized spiked harmonic oscillator Hamiltonians H = −d²/dx² + x² + A/x² + λ/x^α(A ⩾ 0, 2γ > α, γ = 1 + 1/2√1 + 4A) and small values of the coupling λ > 0, are developed. Upper and lower bounds for the eigenvalues are computed by the procedure of Burrows et al (1987 J. Phys. A: Math. Gen.20 889–97) for assessing the accuracy of a truncated perturbation expansion. Closed-form sums for some related perturbation double infinite series then immediately follow as a result of this investigation.

In this paper, we characterize all the Darboux polynomials of the Rabinovich system, = hy − v₁x + yz, = hx − v₂y − xz and ż = −v₃z + xy. Moreover, we give the necessary and sufficient conditions in order that the Rabinovich system has a rational first integral or an algebraic first integral.

We discuss the question of entanglement versus separability of pure quantum states in direct product Hilbert spaces, and the relevance of the issue to physics. Different types of separability may be possible, depending on the particular factorization of the Hilbert space. A given orthonormal basis set for a Hilbert space is defined to be of type (p, q) if p elements of the basis are entangled and q are separable, relative to a given bi-partite factorization of that space. We conjecture that not all basis types exist for a given Hilbert space.

Consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit. We give the distillable entanglement, the number of Bell pairs distilled per copy, as a function of an error exponent, which represents the rate of decrease in failure probability as n tends to infinity. The formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration, which is the well-known entropy of entanglement, and the maximum attained in deterministic concentration. The method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate. In addition to the probabilistic argument, we consider another type of entanglement concentration scheme, where the initial state is deterministically transformed into a (possibly mixed) final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit. We show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity. Furthermore, we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit (strong converse), and give the explicit formulae for those cases.

The parameter changes resulting from a combination of Lorentz transformations are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant which correlates the evolution of parameters.

In the light of the ϕ-mapping topological current theory, the Mermin–Ho vortices and the monopoles in three-component spinor BEC are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents which can be derived from the same field tensor k_μν, and both these topological structures are characterized by the ϕ-mapping topological numbers—Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of Mermin–Ho vortices and the generation and annihilation of monopoles are also discussed.

The nonlinear Rayleigh instability of the cylindrical interface between the vapour and liquid phases of a fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple expansion is used for the investigation. The evolution of amplitude is shown to be governed by a first-order nonlinear differential equation. The stability criterion is discussed, and the region of stability is displayed graphically.