Table of contents

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of the Renormalization Group as featured in the international workshop Renormalization Group 2005, Helsinki, Finland 30 August–3 September 2005 (http://theory.physics.helsinki.fi/~rg2005/). Participants at that meeting as well as other researchers working in the field are invited to submit a research paper to this issue.

The Editorial Board has invited Juha Honkonen, Dmitri Kazakov and Hans Werner Diehl 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 the subject of the workshop.

• 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

  • contain significant additional new results and/or insights or

  • 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.

The guidelines for the preparation of contributions are as follows:

• The DEADLINE for submission of contributions is 1 December 2005. This deadline will allow the special issue to appear in June 2006.

• There is a nominal page limit of 16 printed pages 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 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—Renormalization Group 2005'. Submissions should ideally be in standard LaTeX form. 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—Renormalization Group 2005'.

• 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. Each participant at the workshop and the corresponding author of each contribution will receive a complimentary copy of the issue.

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model.

In a general setting, we introduce a new bipartite state property sufficient for the validity of the perfect correlation form of the original Bell inequality for any three bounded quantum observables. A bipartite quantum state with this property does not necessarily exhibit perfect correlations. The class of bipartite states specified by this property includes both separable and nonseparable states. We prove analytically that, for any dimension d ⩾ 3, every Werner state, separable or nonseparable, belongs to this class.

The computational complexity of the 'cluster minimization problem' is revisited (Wille and Vennik 1985 J. Phys. A: Math. Gen.18 L419). It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analogue of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.

A square lattice directed path confined to a wedge with vertex angle α exerts an entropic force F_α on the wedge. We show that this is a repulsive force of magnitude This force is determined by examining the combinatorial properties of the directed path and by determining the exact entropic contribution to the free energy in the limit as the path length goes to infinite.

Consider a model of partially directed paths from the origin in the square lattice, constrained to the region between the Y-axis and the line Y = qX, and ending in a vertex in this line (with coordinates of the form (N, Nq), and where q > 0 is an integer). Such paths are bargraph paths in a q-wedge. In this paper the adsorption of bargraph paths in the line Y = qX is examined. This model has generating function g_q(t, z) where t is the edge generating variable and z is the generating variable of visits of the path to the line Y = qX. It is proven that the model undergoes an adsorption transition at the critical value of z_q and that z_q is given asymptotically by In other words, z_q/q is given to decaying terms. Moreover, adsorbing bargraph paths in a 1/p-wedge between the Y-axis and the line Y = (1/p)X, where p > 0 is an integer, are also considered. In these models it is shown that z_1/p ≃ p²/2 log p² for large p.

The Helfrich expression for the isotropic membrane bending energy was generalized for the case of anisotropic membranes by taking into account two intrinsic (spontaneous) curvatures, i.e., the intrinsic mean curvature H_m and the intrinsic curvature deviator D_m. Using this generalized expression for the membrane bending energy the shape equation for closed axisymmetric anisotropic membranes is solved numerically for the case of undulated tubular shapes. It is shown that the variation of one of the two intrinsic curvatures, H_m or D_m, may induce the first-order-like shape transitions between the undulated tubular membrane structures. The predicted discontinuous shape transitions were applied to explain the beading transitions without stretching, which were recently observed in nerve fibres.

A usual loop algebra, not necessarily the matrix form of the loop algebra , is also made use of for constructing linear isospectral problems, whose compatibility conditions exhibit a zero-curvature equation from which integrable systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic-form identity is created in the present paper whose special case is just the trace identity; that is, when taking the loop algebra , the quadratic-form identity presented in this paper is completely consistent with the trace identity.

For manifolds of noncompact type endowed with an affine connection (for example, the Levi–Civita connection) and a closed 2-form (magnetic field), we define a Hilbert algebra structure in the space and construct an irreducible representation of this algebra in . This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions, this algebra is unique. The non-commutative product over is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals that this product has a front, which is described in terms of geodesic triangles in . The quantization of δ-functions induces a family of symplectic reflections in and generates a magneto-geodesic connection Γ on . This symplectic connection entangles, on the phase space level, the original affine structure on and the magnetic field. In the classical approximation, the ℏ²-part of the quantum product contains the Ricci curvature of Γ and a magneto-geodesic coupling tensor.

An algebraic solution for the hydrogen atom analogous to the one recently proposed to solve the relativistic version of the system is presented. We add to the usual radial description of the problem an additional angular variable and an associated operator which can be considered as part of an su(1, 1) Lie algebra. The operators of the algebra define radial ladder operator relating the eigenfunctions of the system in unit steps of the principal quantum number. We conclude that the radial bound states of the hydrogen atom in our extended configuration space can be regarded as spanning the minimal M representation of the su(1, 1) Lie algebra. The method can also be extended to solve the s-wave Morse problem and the three-dimensional harmonic oscillator.

Trapped and laser-cooled ions are increasingly used for a variety of modern high-precision experiments, frequency standard applications and quantum information processing. Therefore, in this communication we present a comprehensive analysis of the pattern of information entropy arising in the time evolution of an ion interacting with a laser field. A general analytic approach is proposed for a three-level trapped-ion system in the presence of the time-dependent couplings. By working out an exact analytic solution, we conclusively analyse the general properties of the von Neumann entropy and quantum information entropy. It is shown that the information entropy is affected strongly by the time-dependent coupling and exhibits long time periodic oscillations. This feature attributed to the fact that in the time-dependent region Rabi oscillation is time dependent. Using parameters corresponding to a specific three-level ionic system, a single beryllium ion in a RF-(Paul) trap, we obtain illustrative examples of some novel aspects of this system in the dynamical evolution. Our results establish an explicit relation between the exact information entropy and the entanglement between the multi-level ion and the laser field. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion/field and on the values of Lamb–Dicke parameter η.

The quantum dynamics of a two-level system coupled to a shape-invariant potential is investigated. Shape-invariant potentials share an integrability condition called shape invariance which identifies an underlying algebraic structure, in general infinite dimensional, that transforms the potential parameters such as strength, range and diffuseness. We determine the time-evolution operator, the density operator of the system, and obtain the temporal behaviour of various dynamical variables by considering either pure or mixed initial states of the system, constructed with the generalized coherent state of the shape-invariant coupling potential. We consider specific examples of shape-invariant coupling potentials (harmonic oscillator, Pöschl–Teller and self-similar potentials). The results obtained for all dynamical variables exhibit rapid oscillations which periodically collapse and regenerate in different ways depending on the coupling potential nature.

We present a parametrically efficient method for measuring the entanglement of formation E_f in an arbitrarily given unknown two-qubit state ρ_AB by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E_f.

In this paper, we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the infinite line (Carteret et al2003 J. Phys. A: Math. Gen.36 8775–95). We obtain uniformly convergent asymptotics for the 'exponential decay' regions at the leading edges of the main peaks in the Schrödinger (or wave mechanics) picture. This calculation required us to generalize the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.

We propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator-valued measure on quantum phase. In particular, we construct W^m class, GHZ^m, and GHZ^m−1 class concurrences for general pure m-partite states. We give explicit expressions for W³ and GHZ³ class concurrences for general pure three-partite states and for W⁴, GHZ⁴ and GHZ³ class concurrences for general pure four-partite states.

A simple one-dimensional quantum system with two attractive δ-function potentials of strength q at x ± 1 is subjected to a spatially asymmetric (as in the dipole interaction) harmonic forcing with frequency ω. The time evolution of the system, which has two discrete energy levels −ω_s < −ω_a (depending on q) and a continuum spectrum, exhibits a rich dynamics including regimes where the rate of ionization becomes very small due to the 'inverse' Ramsauer effect in electron–atom collisions. The two-photon ionization with ω ≈ ω_s/2 can be enhanced when ω_a = ω_s/2 though the one-photon ionization is not affected significantly by the location of excited level. When ω is very close to the one- or two-photon resonance the ionization rate can differ greatly from that given by the low order perturbation theory even for small forcing amplitude. This is caused in part by the fact that the dynamic Stark effect has a strong dependence on ω and may shift the resonance frequencies ω_s, ω_a up and down. When the ground state decays faster than the excited state and ω is not close to ω_s − ω_a, the excited level at late times becomes and remains more populated than the ground state. The occupations of the bound states oscillate with a frequency that can be quite low compared with ω, in particular in the case ω ≈ ω_a ≈ ω_s/2, but it approaches ω when ω ≫ ω_s.

Our analysis is based on the analytic structure of the wavefunction's Laplace transform in time. It considers one- and two-'photon' processes; the higher order multiphoton processes can also be treated by our computational scheme which goes beyond the low order perturbation theory.

By using the concept of negativity, we study entanglement in spin-1 Heisenberg chains. Both the bilinear chain and the bilinear–biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and in the 2-spin bilinear–biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.

A generalization of the concept of a system of non-holonomic constraints to fibred manifolds with n-dimensional bases is considered. Motion equations in both Lagrangian and Hamiltonian settings for systems subjected to such constraints are investigated. Regularity conditions for the existence of a non-holonomic Legendre transformation, and the corresponding formulae for Hamiltonian and momenta are found. In particular, Lagrangian constraints and semi-holonomic constraints, and simplifications arising in this case are discussed.

In this work, we reveal hidden symmetries on the nonrelativistic and relativistic description of rotational fluid model. Gauge symmetries will be revealed in the context of the symplectic embedding formalism, which allows us to unveil a set of dynamically equivalent hidden symmetries and extra hidden symmetry.

The Whightman function, the vacuum expectation values of the field square and the energy–momentum tensor are investigated for a scalar field inside a wedge with and without a coaxial cylindrical boundary. Dirichlet boundary conditions are assumed on the bounding surfaces. The vacuum energy–momentum tensor is evaluated in the general case of the curvature coupling parameter. Making use of a variant of the generalized Abel-Plana formula, expectation values are presented as the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the presence of this boundary. The asymptotic behaviour of the field square, vacuum energy density and stresses near the boundaries are investigated. The additional vacuum forces acting on the wedge sides due the presence of the cylindrical boundary are evaluated and it is shown that these forces are attractive. As a limiting case, the geometry of two parallel plates perpendicularly intersected by a third one is analysed.

The maximum-entropy distribution functions applied to Callaway's model for phonon gas dynamics lead to a hierarchy of closed systems of moment equations. The system of equations for the energy density and the heat flux is the first member of this hierarchy of closures. Here emphasis is placed on analysing the next member, the 9-moment maximum-entropy system that involves the flux of the heat flux as an extra gas-state variable. After presenting a study of the one-dimensional, rotationally symmetric reduction of this system, we explicitly calculate a single generating function of three Lagrange multipliers in terms of which the reduced system of three evolution equations for these multipliers can be cast into a symmetric hyperbolic form. In the context of determining the Lagrange multipliers as explicit functions of the moment densities, we discuss new aspects of the expansion of various non-equilibrium quantities about quasi-equilibrium states. This expansion is fundamentally a non-equilibrium expansion that includes the heat flux in a non-perturbative manner, i.e., there are no unphysical limitations on the magnitude of the nonvanishing component of the heat flux to maintain a theory. Results are presented both at the first order in the expansion and at the second order. This enables us to verify the internal consistency of our approach and to justify the non-equilibrium generalization of the method of Grad.

In this paper, we consider the equations governing an inviscid, thermally non-conducting fluid of infinite electrical conductivity in the presence of a magnetic field and subject to no extraneous force. By using conveniently the Lie point symmetries admitted, we map the governing system into an equivalent autonomous form. The transformed system can be directly inspected in order to find some simple solutions that, written in terms of the original variables, provide non-trivial exact solutions of the system at hand. Use is made of some finite transformations known in the literature as substitution principles, enabling us to build exact solutions containing some arbitrary functions. The link between the substitution principle and the recently discovered Bogoyavlenskij symmetries for equilibrium magnetohydrodynamics is also discussed. Some of the recovered solutions are considered to solve well-known physically relevant boundary value problems and the linear stability analysis is performed, thus generalizing well-established results.