Table of contents

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of Quantum Theory and Symmetries as featured in the conference `5th International Symposium on Quantum Theory and Symmetries', University of Valladolid, Spain, July 22–28 2007 (http://tristan.fam.cie.uva.es/~qts5/). Invited speakers at that meeting as well as other researchers working in the field are invited to submit a research paper to this issue. Please note that papers from speakers presenting contributed talks will be published separately in a volume of Journal of Physics Conference Series.

Editorial policy

The Editorial Board has invited Manuel Gadella, José Manuel Izquierdo, Sengül Kuru, Javier Negro and Mariano A del Olmo to serve as Guest Editors for the special issue. Their criteria for the acceptance of contributions are as follows:

•The subject of the paper should relate to the subject of the workshop (see list of topics in the website of the conference http://tristan.fam.cie.uva.es/~qts5/)

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

•Conference papers may be based on already published work but should either

(a) contain significant additional new results and/or insights or

(b) give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems.

•Papers submitted by non-participants should be original and contain substantial new results.

Guidelines for preparation of contributions

•The deadline for contributed papers will be 30 October 2007. This deadline will allow the special issue to appear in June 2008.

•There is a nominal page limit of 16 printed pages (approximately 9600 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical 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 email to jphysa@iop.org, quoting `JPhysA Special Issue—QTS5'. Submissions should ideally be in standard LaTeX form. Please see the website 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 electronic code on floppy disk if available and quoting `JPhysA Special Issue—QTS5'.

•All contributions should be accompanied by a read-me file or covering letter giving the postal and email 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 versions of the journal. Each participant at the workshop and the corresponding author of each contribution will receive a complimentary copy of the issue.

We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two-dimensional (2D) spatial region, in the presence of a uniform magnetic field perpendicular to the 2D plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.

We show explicitly that the perturbative SU(N) Chern–Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern–Simons theory are carried out using the Penner model, and it turns out to be simpler and transparent. It is also shown that the connected correlators of the puncture operator in the Penner model are related to the connected correlators of the operator that gives the Wilson loop operator in the conjugacy class.

We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov–Fokker–Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker–Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step.

It is shown that errors on qubits caused by spatially correlated noise of quantum Brownian motion can be corrected with a stabilizer code (a quantum error correction code) and recovery operations prepared for uncorrelated noise without modifications. The analysis is made by means of the quantum stochastic Liouville equation approach which has been developed within the canonical operator formalism for dissipative systems called non-equilibrium thermo field dynamics. This approach yields a transparent procedure to derive completely positive maps describing errors on qubits under given statistics of noise.

This paper derives a solution to the Navier–Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier–Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier–Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary.

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

We derive an integral convex combination of product states for a range of separable Werner states. Our method consists of expanding the sought-after local density operators in terms of Wigner operators. For dimension d = 2, our decomposition holds for the whole separable range of Werner states, while for d > 2 it is valid for a subset of separable Werner states. We illustrate the general method with the explicit examples d = 2 and d = 3.

In 1980, Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a τ-function of the sixth Painlevé system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-classical weights, for which the diagonal Ising correlations arise as the leading coefficient of the polynomials specialized appropriately. Here we demonstrate that the next-to-diagonal correlations of the anisotropic Ising model are evaluated as one of the elements of this isomonodromic system or essentially as the Cauchy–Hilbert transform of one of the bi-orthogonal polynomials.

We investigate whether the floating phase (where the correlation length is infinite and the spin–spin correlation decays algebraically with distance) exists in the temperature (T)—frustration parameter (κ) phase diagram of 2D ANNNI model. To identify this phase, we look for the region where (i) finite size effect is prominent and (ii) some relevant physical quantity changes somewhat sharply and this change becomes sharper as the system size increases. For κ < 0.5, the low-temperature phase is ferromagnetic and we study energy and magnetization. For κ > 0.5, the low-temperature phase is antiphase and we study energy, layer magnetization, length of domain walls running along the direction of frustration, number of domain-intercepts that are of length 2 along the direction of frustration, and the number of domain walls that do not touch the upper and/or lower boundary. In agreement with some previous studies, our final conclusion is that the floating phase exists, if at all, only along a line.

For a discrete, translationally invariant ϕ⁴ model introduced by Barashenkov et al (2005 Phys. Rev. E 72 35602R), we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a Jacobi elliptic function (JEF) solution. The first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed. A set of JEF solutions, including the staggered ones, is derived. We also report on the stability analysis for the static bounded solutions and exemplify the dynamical behaviour of the unstable solutions. This work provides a road map, through this illustrative example, on how to fully analyse translationally invariant models in terms of their static problem, its first integral, their full set of static solutions and associated conservation laws.

This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler–Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler–Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl.272 368, 2006 J. Phys. A: Math. Gen.39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations.

In quasi-exactly solvable problems partial analytic solutions (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are obtained at a given energy for a special set of values of the potential parameters. To obtain a larger solution space one varies the energy over a discrete set (the spectrum) by simply changing the value of a given integer. A unified treatment that includes the standard as well as the new class of quasi-exactly solvable problems is presented and a few examples are given. The solution space is spanned by discrete square integrable basis functions in which the matrix representation of the Hamiltonian is tridiagonal. Consequently, the wave equation gives a three-term recursion relation for the expansion coefficients of the wavefunction. Imposing quasi-exact solvability constraints results in a complete reduction of the representation to the direct sum of a finite and an infinite component. The finite is real and exactly solvable, whereas the infinite is complex and associated with zero norm states. Consequently, the whole physical space contracts to a finite-dimensional subspace with normalizable states.

We classify all the global phase portraits of the cubic polynomial vector fields of Lotka–Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincaré disc up to a reversal of sense of all orbits.

A detailed analysis of the wave-mode structure in a bend and its incorporation into a stable algorithm for calculation of the scattering matrix of the bend is presented. The calculations are based on the modal approach. The stability and precision of the algorithm is numerically and analytically analysed. The algorithm enables precise numerical calculations of scattering across the bend. The reflection is a purely quantum phenomenon and is discussed in more detail over a larger energy interval. The behaviour of the reflection is explained partially by a one-dimensional scattering model and heuristic calculations of the scattering matrix for narrow bends. In the same spirit, we explain the numerical results for the Wigner–Smith delay time in the bend.

A generalization of the Gram–Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.

We discuss two different incompatible Poisson pencils for the Toda lattice by using known variables of separation proposed by Moser and by Sklyanin.

We extend the range of the searchlight problem in radiative transfer to include internal reflection arising from Fresnel and Lambert processes. For an isotropic beam and a normal beam, we calculate the albedo, the surface intensity and the mean distance of travel of a photon in the lateral direction. Numerical and graphical results are presented for the above quantities.

We study the Dirac equation with a tensor potential which contains a term linear in r and a Coulomb-like term. The eigenstates and eigenvalues are obtained exactly. We found that the energy spectrum and the degeneracy of the levels depend on the alignment of spin with the orbital angular momentum. For parallel alignment, the second term in the potential makes no contribution to the energy levels.

A class of bound-state problems which represents the coupling of a three-level atom with a two-dimensional system involving two shape-invariant potentials is introduced. We consider second-order parasupersymmetric quantum-mechanical models and, using an algebraic formulation for shape-invariant potential systems, resolve the eigenvalue problem for these coupled systems considering two possible kinds for the coupling Hamiltonian (linear and nonlinear in the potential ladder operators). An application is given for a couple of shape-invariant potentials (harmonic oscillator + Morse potentials).

We compute rigorously the ground and equilibrium states for Kitaev's model in 2D, both the finite and infinite versions, using an analogy with the 1D Ising ferromagnet. Next, we investigate the structure of the reduced dynamics in the presence of thermal baths in the Markovian regime. Special attention is paid to the dynamics of the topological freedoms which have been proposed for storing quantum information.

We study the effect of a constant uniform magnetic field on an electrically charged massive particle (an electron) bound by a potential well, which is described by means of a single attractive λδ(r) potential. A transcendental equation that determines the electron energy spectrum is derived and solved. The electron wavefunction in the ground (bound) state is approximately constructed in a remarkably simple form. It is shown that there arises the probability current in the bound state in the presence of a uniform constant magnetic field. This (electric) current, being by the gauge invariant quantity, must be observable and involve (and exercise influence on) the electron scattering. The probability current density resembles a stack of 'pancake vortices' whose circulating 'currents' around the magnetic field direction (z-axes) are mostly confined within the plane z = 0. We also compute the tunnelling probability of an electron from the bound to free state under a weak constant homogeneous electric field, which is parallel to the magnetic field. The model under consideration is briefly discussed in two spatial dimensions.

In this paper the geometry of two-qubit systems under a local unitary group SO(2) ⊗ SU(2) is discussed. It is shown that the quaternionic conformal map intertwines between this local unitary subgroup of Sp(2) and the quaternionic Möbius transformation which is rather a generalization of the results of Lee et al (2002 Quantum Inf. Process.1 129).

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated with the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Pöschl–Teller potentials.

We start with a given modular invariant of a two-dimensional conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, (1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; (2) the quantum symmetries of the higher ADE graph G associated with the initial modular invariant . Note that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyse several exceptional cases at levels 5 and 9.

Microwave vortices in ferrite particles can appear in different kinds of physical phenomena depending on space scales of the wave processes. In this paper, we show that the vortex states can be created not only in magnetically soft 'small' (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated 'big' (when the exchange fluctuations are neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disc with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case, the scalar (magnetostatic-potential) wavefunctions may have a phase singularity in the centre of a dot. A non-zero azimuth component of the flow velocity demonstrates the vortex structure. The vortices are guaranteed by the chiral edge states of magnetic-dipolar modes in a quasi-2D ferrite disc.