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.

This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand canonical density matrix involving a complete commuting set of observables including the Hamiltonian. The result obtained, which is derived for a generic finite-dimensional quantum system, shows that the equilibrium state arising from unitary evolution is always expressible in the canonical form, without the consideration of a system-bath decomposition.

In distinction to the Neumann case, the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold resonances. Our main point in this paper is to show that modifying locally the geometry we can achieve in the limit a nontrivial coupling between the edges including, in particular, the class of δ-type boundary conditions. We work out an illustration of this claim in the simplest case when a bent waveguide is squeezed.

It is well known that the CP violating theta term of QCD can be converted to a phase in the quark mass term. However, a theory with a complex mass term for quarks can be regularized so as not to violate CP, for example through a zeta function. The contradiction is resolved through the recognition of a dependence on the regularization or measure. The appropriate choice of regularization is discussed and implications for the strong CP problem are pointed out.

We address the generalized measurement of the two-boson operator Z_γ = a₁ + γa†₂ which, for |γ|² ≠ 1, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly construct the minimal Naimark extension, which involves a single additional bosonic system, and present its decomposition in terms of two-boson linear SU(2) interactions. The statistics of the measurement and the added noise are analysed in detail. Results are exploited to revisit the Caves–Shapiro concept of generalized phase observable based on heterodyne detection.

We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector universality class for N = 0. We obtain , where is normalized so that the three-dimensional field-theoretical β function behaves as for small . As a byproduct, we also obtain precise estimates of the interpenetration ratio Ψ*, Ψ* = 0.246 85(11) and of the exponent ν, ν = 0.5876(2).

We find that the modified sine-Gordon equation belonging to the class of the soliton equations describes the propagation of extremely short transverse acoustic pulses through the low-temperature crystal containing paramagnetic impurities with effective spin in the Voigt geometry case. The features of nonlinear dynamics of strain field and effective spins, which correspond to the different kinds of acoustic solitons, are studied.

It is shown that a (1 + 1)-dimensional lattice Boltzmann discretization of the Klein–Gordon and Dirac equations complies with equal-time-commutation-relations. As a result, the lattice Boltzmann discretization leads to a consistent lattice formulation of the quantum field theory in 1 + 1 dimensions. The present kinetic approach may offer a significant simplification over previous Hamiltonian formulations, because the quantum fields move along simple classical trajectories defined by the causal lightcones. This should facilitate both analytical manipulations and symbolic computer implementations of the method.

Starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in Talkner et al (2007 Phys. Rev. E 75 050102 (Preprint cond-mat/0703213)) the quantum version of the Crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation.

The rotational diffusion of a general-shape object (a molecule) in a flow of uniaxial nematic liquid crystal is considered in the molecular field approximation. The full corresponding Fokker–Planck equation is derived, and then reduced to the limit of diffusion of orientational coordinates in a field of uniaxial nematic potential and the flow gradient. The spectrum of orientational relaxation times follows from this analysis. As a second main theme of this work, we derive a complete form of microscopic stress tensor for this molecule from the first principles of momentum balance. Averaging this microscopic stress with the non-equilibrium probability distribution of orientational coordinates produces the anisotropic part of the continuum Leslie–Ericksen viscous stress tensor and the set of viscous coefficients, expressed in terms of molecular parameters, nematic order and temperature. The axially-symmetric limits of long-rod and thin-disc molecular shapes allow comparisons with existing theories and experiments on discotic viscosity. The review concludes with more complicated aspects of nonlinear constitutive equations, microscopic theory of rotational friction and the case of non-uniform flow and director gradients.

In this paper, we propose a general way of computing expectation values in the zero-range process (ZRP), using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux–density plot) of the asymmetric exclusion process corresponding to the ZRP. We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand-canonical ensemble.

We study the size and the lifetime distributions of scale-free random branching trees in which k branches are generated from a node at each time step with probability q_k ∼ k^−γ. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number C = ∑_kkq_k is larger than 1. The tree-size distribution p(s) exhibits a crossover behaviour when 2 < γ < 3. A characteristic tree size s_c exists such that for s ≪ s_c, p(s) ∼ s^{−γ/(γ−1)} and for s ≫ s_c, p(s) ∼ s^−3/2exp(−s/s_c), where s_c scales as ∼(C − 1)^{−(γ−1)/(γ−2)}. For γ > 3, it follows the conventional mean-field solution, p(s) ∼ s^−3/2exp(−s/s_c) with s_c ∼ (C − 1)⁻². The lifetime distribution is also derived. It behaves as ℓ(t) ∼ t^{−(γ−1)/(γ−2)} for 2 < γ < 3, and ∼t⁻² for γ > 3 when branching step t ≪ t_c ∼ (C − 1)⁻¹, and ℓ(t) ∼ exp(−t/t_c) for all γ > 2 when t ≫ t_c. The analytic solutions are corroborated by numerical results.

Path integral Monte Carlo simulations have been carried out for a system of interacting fermionic particles in one dimension. Due to the fact that the sign problem can be completely eliminated for one-dimensional systems, such simulations allow one to obtain accurate energies and particle densities in arbitrary external potentials. Two cases were considered: electrons in the field of a uniform neutralizing background and in an effective field of atoms on a lattice. In the latter case, a clear asymmetry of the charge density distribution of conducting electrons and holes has been observed.

The initial value problem for a class of reversible elementary cellular automata with periodic boundaries is reduced to an initial-boundary value problem for a class of linear systems on a finite commutative ring . Moreover, a family of such linearizable cellular automata is given.

We present a Grünwald–Letnikov implicit finite difference method to solve the space-fractional Fokker–Planck equation with natural boundary condition. Then the properties of aperiodic stochastic resonance in the presence of Lévy noise are investigated in theory and tested by simulation. It is shown that aperiodic stochastic resonance does occur in the presence of Lévy noise, but is reduced by the lower Lévy index α. With the optimal system parameters, the probability of detection error decreases with the decrease of α. Therefore, the performance of a bistable system is improved by the lower index α of Lévy noise.

In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic solutions and we study their dynamics. Moreover, we find three invariant sets of dimension four where the flow is integrable.

In this paper, the classical theory of spherical harmonics in is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk–Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace, and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.

The singular manifold method is used to generate lump solutions of a generalized integrable nonlinear Schrödinger equation in 2 + 1 dimensions. We present several essentially different types of lump solutions. The connection between this method and the Ablowitz–Villarroel scheme is also analysed.

The widely investigated question 'Can one hear the shape of a drum?' which Kac posed in his published lecture (Kac 1966 Am. Math. Mon.73 1–23) was eventually answered negatively in Gordon et al (1992 Invent. Math.110 1–22) by construction of isospectral pairs in . Up to present, all known planar counter examples are constructed by a certain tiling method, and in this communication, we call such examples isospectral Euclidean TI-domains. From counter examples of this type, one can construct a pair of (finite) involution graphs. In this communication, we address the question as to how the isospectrality of the domains for the Laplacian influences the cospectrality of the involution graphs.

The relation between Radon transform and orthogonal expansions of a function on the unit ball in is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.

Two results are proved at the quantal level in Sorkin's hierarchy of measure theories. One is a strengthening of an existing bound on the correlations in the EPR-Bohm set-up under the assumption that the probabilities admit a strongly positive joint quantal measure. It is also proved that any set of no-signalling probabilities, for two distant experimenters with a choice of two alternative experiments each and two possible outcomes per experiment, admits a joint quantal measure, though one that is not necessarily strongly positive.

A second-order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second-order partner Hamiltonians may be exploited to obtain a simple shape-invariant condition. Indeed, a novel relation between potential and mass functions is derived, which leads to a class of exactly solvable models. As an illustration of our procedure, two examples are given for which one obtains whole spectra algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like or singular-oscillator-like spectra depending on the values of the shape-invariant parameter.

The quantum entanglement of the ground state and the thermal entanglement of the mixed thermal state of a three-qubit system with the Heisenberg interaction are investigated in detail in the presence of an inhomogeneous magnetic field. The concurrence of the model is compared with the magnetization, and the threshold temperature of the entanglement is discussed. The effects of the magnetic field and the coupling coefficient in the thermal entanglement are also examined by considering the concurrence of the three-qubit and two-qubit systems. We found that the thermal entanglement of the system exists at temperatures below the threshold temperature even if the ground state is unentangled.

The nonrelativistic quantum scattering problem for a non-central potential which belongs to a class of potentials exhibiting an 'accidental' degeneracy is studied. We show that the scattering system under consideration admit the Lie algebra as the potential algebra. The scattering amplitude is then evaluated using purely algebraic techniques to give the closed result. It is expressed in terms of associated Legendre functions.

We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to the regime in which fermion number is superselected. This work is a further elaboration of work by Colin, in which a Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend his work to non-electromagnetic interactions, we discuss a cut-off regularization of the pilot-wave model and study how it reproduces the standard quantum predictions. The Dirac sea pilot-wave model can be seen as a possible continuum generalization of a lattice model by Bell. It can also be seen as a development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who also suggested the use of the Dirac sea for the development of a pilot-wave model for quantum electrodynamics.

Using the general expressions for level shifts obtained from the master equation for a small system interacting with a large one considered as a reservoir, we calculate the dispersive potentials between an atom and a wall in the dipole approximation. We analyse in detail the particular case of a two-level atom in the presence of a perfectly conducting wall. We study the van der Waals as well as the resonant interactions. All distance regimes as well as the high and low temperature regimes are considered. We show that the Casimir–Polder interaction cannot be considered as a direct result of the vacuum fluctuations only. Concerning the interaction between the atom and the wall at high temperatures, we show that a saturation of the potential for all distances occurs. This saturated potential coincides precisely with that obtained in the London–van der Waals limit.

In a previous paper, we found that in the context of the string theory 'discretuum' proposed by Bousso and Polchinski, the cosmological constant probability distribution varies wildly. However, the successful anthropic predictions of the cosmological constant depend crucially on the assumption of a flat prior distribution. We conjectured that the staggered character of our Bousso–Polchinski distribution will arise in any landscape model which generates a dense spectrum of low-energy constants from a wide distribution of states in the parameter space of the fundamental theory. Here we calculate the volume distribution for Λ in the simpler Arkani-Hamed–Dimopolous–Kachru landscape model, and indeed this conjecture is borne out.

Some features of the calculation of fluid dynamo systems (spherically symmetric α²-dynamos) in magnetohydrodynamics are studied, the problem connected with the presence of mixed (Robin) boundary conditions is addressed and a new treatment for it is proposed. The perturbation formalism of large-ℓ expansions is shown to be applicable and its main technical steps are outlined.