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 Pseudo Hermitian Hamiltonians in Quantum Physics as featured in the conference '6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics', City University London, UK, July 16--18 2007 (http://www.staff.city.ac.uk/~fring/PT/). Invited speakers 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 Andreas Fring, Hugh F Jones and Miloslav Znojil 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 ((see list of topics in the website of the conference http://www.staff.city.ac.uk/~fring/PT/).

•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 the following:

•The DEADLINE for submission of contributions is 16 November 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 e-mail to jphysa@iop.org, quoting 'JPhysA Special Issue—PHHQP07'. 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 the electronic code on CD if available and quoting 'JPhysA Special Issue---PHHQP07'. 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.

There exists a well-known duality between the Maxwell–Chern–Simons theory and the 'self-dual' massive model in (2 + 1) dimensions. This dual description may be extended to topologically massive gauge theories (TMGT) for forms of arbitrary rank and in any dimension. This communication introduces the construction of this type of duality through a reparametrization of the 'master' theory action. The dual action thereby obtained preserves the full gauge symmetry structure of the original theory. Furthermore, the dual action is factorized into a propagating sector of massive gauge-invariant variables and a decoupled sector of gauge-variant variables defining a pure topological field theory. Combining the results obtained within the Lagrangian and Hamiltonian formulations, a completed structure for a gauge-invariant dual factorization of TMGT is thus achieved.

We describe a nano-electro-mechanical system that exhibits the 'retroactive' quantum jumps discovered by Mabuchi and Wiseman (1998 Phys. Rev. Lett.81 4620). This system consists of a Cooper-pair box coupled to a nano-mechanical resonator, in which the latter is continuously monitored by a single-electron transistor or quantum point contact. Further, we show that these kinds of jumps, and the jumps that emerge in a continuous quantum non-demolition measurement, are one and the same phenomena. We also consider manipulating the jumps by applying feedback control to the Cooper-pair box.

Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces in with a slow modulation is proposed. Integrable deformations of such surfaces are described by the dispersionless Davey–Stewartson (DS) hierarchy. Quasiclassical GWRs for other four-dimensional spaces and the dispersionless DS system are discussed too.

The d² Pauli operators attached to a composite qudit in dimension d may be mapped to the vectors of the symplectic module ( being the modular ring). As a result, perpendicular vectors correspond to commuting operators, a free cyclic submodule to a maximal commuting set, and disjoint such sets to mutually unbiased bases. For dimensions d = 6, 10, 15, 12 and 18, the fine structure and the incidence between maximal commuting sets are found to reproduce the projective line over the rings and , respectively.

We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven-diffusive systems—which includes exclusion processes—focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix-product form. In addition to a gentle introduction to this matrix-product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free-energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix-product state for a given model and more complicated variants of the matrix-product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff's matrix-tree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.

We extend a previous statistical mechanical treatment of the traveling salesman problem by defining a discrete 'site-disordered' problem in which fluctuations about saddle points can be computed. The results clarify the basis of our original treatment, and illuminate but do not resolve the difficulties of taking the zero-temperature limit to obtain minimal path lengths.

The birefringence phenomenon in the vacuum with a constant magnetic background of arbitrary strength is considered within the framework of the effective action approach. A new feature of the birefringence in a magnetized vacuum is that the parallel mode, which is polarized parallel to the plane containing the magnetic field and the photon wave vector, is no longer transverse. We have studied this feature in detail for an arbitrary magnetic field and provided analytic results for the ultra-strong magnetic field regime. Possible physical implications of our results in astrophysics are discussed.

A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next reformulate the singularity condition in terms of a flow in the space of an auxiliary one-parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain. Based on this analytic behavior, we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations.

We consider the energy spectra of quantum Hamilton systems whose classical dynamics is of mixed type, i.e. regular for some initial conditions in the classical phase space and chaotic for the complementary initial conditions. In the strict semiclassical limit when the effective Planck constant ℏ_eff is sufficiently small the Berry–Robnik (BR) statistics applies, while at larger values of ℏ_eff (or smaller energies) one sees deviations from BR due to localization and tunneling effects. We derive a two-level random matrix model, which describes these effects and can be treated analytically in a closed form. The coupling between the regular and chaotic levels due to tunneling is assumed to be Gaussian distributed. This two-level model describes most of the features of matrices of large dimensions (here N = 1000), which we treat numerically, and is predicted to apply in mixed type systems at low energies. The proposed analytical level spacing distribution function has two parameters, the BR parameter ρ, characterizing the classical phase space, and the coupling (antenna distortion or tunneling) parameter σ between states. Localization effects so far are not included in our analysis except in the special case where ρ can be replaced by some effective ρ_eff.

We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds (B, g_B) and (F, g_F) furnished with metrics of the form c²g_B ⊕ w²g_F and, in particular, of the type w^2μg_B ⊕ w²g_F, where c, w:B → (0, ∞) are smooth functions and μ is a real parameter. We obtain suitable expressions for the Ricci tensor and scalar curvature of such products that allow us to establish results about the existence of Einstein or constant scalar curvature structures in these categories. If (B, g_B) is Riemannian, the latter question involves nonlinear elliptic partial differential equations with concave–convex nonlinearities and singular partial differential equations of the Lichnerowicz–York-type among others.

We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero–Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the reduced density matrix and the entanglement entropy in the limit of an infinite number of particles traced out. From these results, we obtain an upper-bound value of the entanglement entropy. This upper bound has a clear interpretation in terms of fractional exclusion statistics.

The Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of the 't Hooft–Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.

We study the decoherence of superpositions of displaced quantum states of the form (where |g⟩ is an arbitrary 'fiducial' state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α_k and N. We obtain approximate formulae for an arbitrary state |g⟩ and explicit exact expressions in the special case of |g⟩ = |m⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m. We show that the superposition with a large number of components N and rich 'internal structure' (m ∼ |α|²) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.

We critically examine the quantum-mechanical modelling of a measurement process using the Stern–Gerlach (SG) setup in the most general context, probing in particular for nonideal situations, the subtleties involved in the connection between the notion of 'distinguishability' of apparatus states defined in terms of the inner product and the spatial separation among the wave packets emerging from the SG setup. The quantitative studies highlighting some of the unexplored features of this relationship are presented in terms of an appropriately defined measure for the spatial separation between the emerging wave packets. It is also indicated how the effects arising from such departures from the idealness can be empirically tested for different values of the relevant parameters.

Quantum electrodynamics (QED) fixed in the 't Hooft–Veltman gauge is renormalized to three loops in the scheme. The β-functions and anomalous dimensions are computed as functions of the usual QED coupling and the additional coupling, ξ, which is introduced as part of the nonlinear gauge-fixing condition. Similar to the maximal Abelian gauge of quantum chromodynamics, the renormalization of the gauge parameter is singular.

During the inflationary phase of the early universe, quantum fluctuations in the vacuum generate particles as they stretch beyond the Hubble length. These fluctuations are thought to result in the density fluctuations and gravitational radiation that we can try to observe today. It is possible to calculate the quantum mechanical evolution of these fluctuations during inflation and the subsequent expansion of the universe until the present day. The present calculation of this evolution directly exposes the particle creation during accelerated expansion and while a fluctuation is larger than the Hubble length. Because all fluctuations regardless of their scale today began as the vacuum state in the early universe, the current quantum mechanical state of fluctuations is correlated on different scales and in different directions.

The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in the presence of a viscous fluid and a Λ term, with the spinor field nonlinearity being some arbitrary functions of the invariants I and J constructed from bilinear spinor forms S and P, generates a multi-parametric system of ordinary differential equations (Saha 2005 Rom. Rep. Phys.57 7, Saha 2007 Preprint gr-qc/0703085 (Astrophys. Space Sci. at press)). A qualitative analysis of the system in question has been thoroughly carried out. A complete qualitative classification of the mode of the evolution of the universe given by the corresponding dynamic system has been illustrated.

A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen.39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory.