Table of contents

This is a call for contributions to a special issue ofJournal of Physics A: Mathematical and General entitled `Singular Interactions in Quantum Mechanics: Solvable Models'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with point-interaction models, one- and many-body, quantum graphs, including graph-like structures coupling different dimensions, interactions supported by curves, manifolds, and more complicated sets, random and nonlinear couplings, etc., as well as approximations helping us to understand the meaning of singular couplings and applications of such models on different parts of quantum mechanics. We believe that when the second printing of the `bible' of the field, the book Solvable Models in Quantum Mechanics by S Albeverio, F Gesztesy, the late R Høegh-Krohn and H Holden, appears it is the right moment to review new developments in this area, with the hope of stimulating further development of these extremely useful techniques.

The Editorial Board has invited G Dell'Antonio, P Exner and V Geyler to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows:

• The subject of the paper should relate to singular interactions in quantum mechanics in the sense described above.

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

• Papers should be original; reviews of a work published elsewhere will not be accepted.

The guidelines for the preparation of contributions are as follows:

• The DEADLINE for submission of contributions is 31 October 2004. This deadline will allow the special issue to appear in about April 2005.

• There is a nominal page limit of 15 printed pages (approximately 9000 words) per contribution. 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 by web upload at {www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue-Quantum Mechanics: Solvable Models'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including 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-Quantum Mechanics: Solvable Models'.

• 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 the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

G Dell'Antonio, P Exner and V Geyler

Guest Editors

We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor at small argument, which in turn yields the asymptotic level compressibility for macroscopic correlation lengths.

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformation in each of the variables is determined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established. For the purpose of illustration, a fluid membrane described by a Hamiltonian quadratic in curvature is considered.

Motivated by recent experiments with superradiant Bose–Einstein condensate (BEC) we consider simple microscopic models describing rigorously the interference of the two cooperative phenomena, BEC and radiation, in thermodynamic equilibrium. Our results in equilibrium confirm the presence of the observed superradiant light scattering from BEC: (a) the equilibrium superradiance exists only below a certain transition temperature; (b) there is superradiance and matter–wave (BEC) enhancement due to the coherent coupling between light and matter.

The pair-contact process 2A → 3A, 2A → ∅ with diffusion of individual particles is a simple branching-annihilation process which exhibits a phase transition from an active to an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years, it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.

The kinetics of the q species pair annihilation reaction (A_i + A_j → ∅ for 1 ⩽ i < j ⩽ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as ρ(t) ∼ t^−α. For d = 1 the system segregates into single-species domains, yielding a different value of α for each q; for a simplified version of the model in one dimension we derive α(q) = (q − 1)/(2q). Within mean-field theory, applicable in d ⩾ 2, segregation occurs only for q < 1 + (4/d). The only physical realization of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d ⩾ 2 and q ⩾ 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (α = 1) that also characterizes the single-species annihilation process A + A → ∅.

Properties of constant-speed uniform random walks in bounded convex bodies are presented. Average quantities such as the mean length of the trajectories are expressed only according to the first moments of the chord length distribution. Some analytical results are then extended to the case of purely diffusive random walks. Exact results for convex geometric objects of simple shape in two and three dimensions illustrate our points.

The critical behaviour at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d = 3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Padé resummation techniques. For n < n_c the system belongs to the universality class of the isotropic n-component model, while for n > n_c the cubic fixed point becomes stable, where n_c < 3 is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behaviour of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for n > n_c.

We develop a generic representation-independent contraction procedure for obtaining, for instance, matrices and L operators of arbitrary dimensions for the quantized super-Jordanian algebra from the pertinent quantities of the standard q-deformed algebra.

A DNA sequence can be identified with a word over the alphabet Σ = {A, C, G, T}. An algebraic method is used to analyse DNA sequences and their three-dimensional vector representation, and, via their geometric representation, an equivalence relation on DNA sequences is introduced, and the number of equivalence classes of sequences is counted. Finally, a kind of inequality involving equivalent sequences' entropy is proved.

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time t for the KPESCS which, in contrast to the binary Darboux transformation of the KP equation, provides a non-auto-Bäcklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.

A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F ∼ (E, B) on the electric current and G ∼ (H, D) on the magnetic current, can be derived from an energy-momentum 'potential' if and only if the constitutive relation G = G(F) satisfies a certain vanishing condition. The electric-magnetic reciprocity introduced by Hehl and Obukhov is shown to define a one-parameter family ⊛_z of complex structures on the product space of 2-form pairs (F, G), independent of any spacetime metric, which reduces to the product of two Hodge star operators once a Lorentzian metric is introduced. In contrast to a recent claim made in the literature, it does not define a complex structure on the space of 2-forms itself.

Ultraviolet finite quantum field theory on even-dimensional noncommutative spacetime is formulated using coordinate coherent states. 2D spacetime is foliated into families of orthogonal, noncommutative, two planes. Lorentz invariance is recovered if one imposes a single noncommutative parameter θ in the theory. Unitarity is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.