<Emphasis Type="Italic">N</Emphasis> = 1 Supersymmetric Sigma Model with Boundaries,I

 We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures. Received: 27 November 2001 / Accepted: 16 August 2002 Published online: 19 December 2002 Acknowledgements. We are grateful to Ingemar Bengtsson and Andrea Cappelli for discussions and comments. MZ would like to thank the ITP, Stockholm University, where part of this work was carried out. UL acknowledges support in part by EU contract HPNR-CT-2000-0122 and by NFR grant 650-1998368. Communicated by R.H. Dijkgraaf     

Mixing and sorting of bidisperse two-dimensional bubbles

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area λ ( λ≤1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of λ, the minimal configuration for N → ∞. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in “phase-separated” clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N,λ). As λ is varied, this alternates between a circular cluster of one of the mixed tilings, and “partial wetting” of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area λ. Received 1 August 2002 RID="a" ID="a"e-mail: paulo@ist.utl.pt     

A Farey Fraction Spin Chain

We introduce a new number-theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation-invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and a phase transition occurs for positive inverse temperature β= 2. The free energy is the same as that of related, non-translation-invariant number-theoretic spin chain. Using a number-theoretic argument, the low-temperature (β > 3) state is shown to be completely magnetized for long chains. The number of states of energy E= log(n) summed over chain length is expressed in terms of a restricted divisor problem. We conjecture that its asymptotic form is (n log n), consistent with the phase transition at β= 2, and suggesting a possible connection with the Riemann ζ-function. The spin interaction coefficients include all even many-body terms and are translation invariant. Computer results indicate that all the interaction coefficients, except the constant term, are ferromagnetic. Received: 20 August 1998/ Accepted: 17 December 1998     

On the Gribov Problem for Generalized Connections

 The bundle structure of the space of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space . However, for a certain class of non-abelian gauge theories – e.g., all SU(N) theories – the generic stratum is nontrivial. This means, there are no global gauge fixings – the so-called Gribov problem. Nevertheless, for many physical measures there is a covering of the generic stratum by trivializations each having total measure 1. Finally, possible physical consequences and the relation between fundamental modular domains and Gribov horizons are discussed. Received: 4 March 2002 / Accepted: 20 August 2002 Published online: 30 January 2003 Communicated by H. Nicolai     

Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

 We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity ν, and grows like ν ^-3 when ν goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time. Received: 14 March 2002 / Accepted: 7 May 2002 Published online: 22 August 2002     

On Noncommutative Multi-Solitons

 We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ²) ^k /S _k . We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ²/ℤ _k , cylinder, and T ² . However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli space provides an explicit K?hler resolution of (ℝ⁴) ^k /S _k . In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ ^d , which for d>2 (and k>3) is not smooth and can have multiple branches. Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002 Communicated by R.H. Dijkgraaf     

Connections on Naturally Reductive Spaces,Their Dirac Operator and Homogeneous Models in String Theory

 Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇ ^t joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D ^t corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D <sup>1/3</sup>. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5-dimensional example. Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002 RID="*" ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft and the Max-Planck Society.     

Surfaces and the Sklyanin Bracket

 We discuss the Lie Poisson group structures associated to splittings of the loop group LGL(N,ℂ), due to Sklyanin. Concentrating on the finite dimensional leaves of the associated Poisson structure, we show that the geometry of the leaves is intimately related to a complex algebraic ruled surface with a ℂ ^*-invariant Poisson structure. In particular, Sklyanin's Lie Poisson structure admits a suitable abelianisation, once one passes to an appropriate spectral curve. The Sklyanin structure is then equivalent to one considered by Mukai, Tyurin and Bottacin on a moduli space of sheaves on the Poisson surface. The abelianization procedure gives rise to natural Darboux coordinates for these leaves, as well as separation of variables for the integrable Hamiltonian systems associated to invariant functions on the group. Received: 8 August 2001/Accepted: 29 April 2002 Published online: 14 October 2002 RID="★" ID="★" The first author of this article would like to thank NSERC and FCAR for their support RID="★★" ID="★★" The second author was partially supported by NSF grant number DMS-9802532     

Higher-Degree Analogs of the Determinant Line Bundle

 In the first part of this paper, given a smooth family of Dirac-type operators on an odd-dimensional closed manifold, we construct an abelian gerbe-with-connection whose curvature is the three-form component of the Atiyah-Singer families index theorem. In the second part of the paper, given a smooth family of Dirac-type operators whose index lies in the subspace of the reduced K-theory of the parametrizing space, we construct a set of Deligne cohomology classes of degree i whose curvatures are the i-form component of the Atiyah-Singer families index theorem. Received: 27 September 2001 / Accepted: 5 April 2002 Published online: 22 August 2002     

Dynamics of a single ion in a perturbed Penning trap. Sextupolar perturbation

In the frame work of classical mechanics, we study the nonlinear dynamics of a single ion trapped in a Penning trap perturbed by an electrostatic sextupolar perturbation. The perturbation is caused by a deformation in the configuration of the electrodes. By using a Hamiltonian formulation, we obtain that the system is governed by three parameters: the z-component of the canonical angular momentum P _φ - which is a constant of the motion because the perturbation we assume is axial-symmetric -, the parameter δ that determines the ratio between the axial and the cyclotron frequencies, and the parameter a which indicates how far from the ideal design the electrodes are. We study the case P _φ = 0. By means of surfaces of section, we show that the phase space structure is made of three fundamental families of orbits: arch, loop and box orbits. The coexistence of these kinds of orbits depends on the parameter δ. The escape is also explained on the basis of the shape of the potential energy surface as well as of the phase space structure. Received 6 September 2001 / Received in final form 19 March 2002 Published online 28 June 2002     

Dimension and Dynamical Entropy for Metrized <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-Algebras

 We introduce notions of dimension and dynamical entropy for unital C ^* -algebras ``metrized' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical coincides with the topological entropy of its commutative analogue. Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002     

Identification of the Mass and Stability Interval of Strong Potential in Heavy Mesons

In this paper, we have calculated the masses of mesons containing t-quark and their spins’ coupling coefficients. This was achieved by solving Lippmann-Schwinger equation for the quark-antiquark bound state of heavy mesons in configuration space. Heavy meson masses submitted criteria for the strong nuclear interactive potential between two quarks. We investigated the stability of a few suitable potentials and offered the best of these potentials for heavy mesons.     

A Hamiltonian Model for Linear Friction in a Homogeneous Medium

 We introduce and study rigorously a Hamiltonian model of a classical particle moving through a homogeneous dissipative medium at zero temperature in such a way that it experiences an effective linear friction force proportional to its velocity (at small speeds). The medium consists at each point in a space of a vibration field modelling an obstacle with which the particle exchanges energy and momentum in such a way that total energy and momentum are conserved. We show that in the presence of a constant (not too large) external force, the particle reaches an asymptotic velocity proportional to this force. In a potential well, on the other hand, the particle comes exponentially fast to rest in the bottom of the well. The exponential rate is in both cases an explicit function of the model parameters and independent of the potential. Received: 18 July 2001 / Accepted: 20 April 2002 Published online: 12 August 2002     

On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

Atomic coherent states studied by virtue of the EPR entangled state and their Wigner functions

Based on the newly constructed Einstein, Podolsky and Rosen (EPR) entangled state representation we introduce macroscopic classical functions associated with atomic coherent state τ with angular momentum value j. These functions are proportional to the ordinary one-variable Hermite polynomials of order 2j. The corresponding Wigner quasiprobability function for τ in phase space is also derived which turns out to be a two-variable Hermite polynomial H _{2j, 2j}. In so doing, a new classical-quantum correspondence scheme for angular momentum system is established. Received 7 August 2002 / Received in final form 14 December 2002 Published online 24 April 2003 RID="a" ID="a"Work supported by the National Natural Science Foundation of China under grant 10175057. RID="b" ID="b"e-mail: fhym@sjtu.edu.en     

Laser-based photoacoustic ammonia sensors for industrial applications

An industrial trace-ammonia sensor based on photoacoustic spectroscopy and CO₂ lasers has been developed for measuring ammonia with a 1σ detection limit of 220 parts-per-trillion (ppt) in an integration time of 30 s. The instrument response time for measuring ammonia was 200 s, limited by adsorption effects due to the polar nature of ammonia. The minimum detectable fractional absorbance was 2.0×10^-7, and the minimum normalized detectable absorption coefficient for this system was 2.4×10^-7 W cm^-1/z. The 9R(30) transition of the CO₂ laser at 9.22 μm with 2 W of output power was used to probe the strong sR(5,K) multiplet of ammonia at the same wavelength. This sensor was demonstrated with an optically multiplexed configuration for simultaneous measurement in four cells. Received: 3 April 2002 / Revised version: 31 May 2002 / Published online: 21 August 2002 RID="*" ID="*"Corresponding author. Fax: +1-310/458-0171, E-mail: webber@pranalytica.com     

New parameterization of the trinucleon wave function and its application to the π <Superscript>3</Superscript>He scattering length

We present a new parameterization of the trinucleon wave function. As a novel feature a separable parameterization for the complete wave function is given. In this way any calculation that considers two-body currents only is largely simplified. To demonstrate this we calculate the π³He scattering length in chiral-perturbation theory. We find reasonable agreement with experimental values inferred from data on level shifts in pionic ³He bound states. The relevance of the π-triton system for an alternative determination of the πN scattering lengths is discussed. Received: 12 August 2002 / Accepted: 25 November 2002 / Published online: 25 February 2003 RID="a" ID="a"e-mail: c.hanhart@fz.juelich.de Communicated by V. Vento     

Lifetime of heavy hypernuclei and its implications on the weak ΛN interaction

The lifetime of the Λ-hyperon in heavy hypernuclei measured in proton-Au, -Bi and -U collisions by the COSY-13 Collaboration at COSY-Jülich has been analyzed to yield τ_Λ = (145±11) ps. This value for τ_Λ is compatible with the lifetime extracted from antiproton annihilation on Bi and U targets, albeit much more accurate. Theoretical models based on the meson exchange picture and assuming the validity of the phenomenological ΔI = 1/2 rule predict the lifetime of heavy hypernuclei to be significantly larger (2-3 standard deviations). Such large differences indicate that at least one of the assumptions in these models is not fulfilled. A much better reproduction of the lifetimes of heavy hypernuclei is achieved in the phase space model, if the ΔI = 1/2 rule is discarded in the nonmesonic Λ decay. Received: 8 August 2002 / Accepted: 20 December 2002 / Published online: 25 March 2003 RID="a" ID="a"e-mail: h.stroeher@fz-juelich.de Communicated by Th. Walcher     

Kähler Moduli Space for a D-Brane at Orbifold Singularities

We develop a method to analyze systematically the configuration space of a D-brane localized at the orbifold singular point of a Calabi–Yau d-fold of the form ℂ ^d /Γ using the theory of toric quotients. This approach elucidates the structure of the K?hler moduli space associated with the problem. As an application, we compute the toric data of the Γ-Hilbert scheme. Received: 9 June 1998 / Accepted: 18 November 1998     

Applications of the modified Faddeev equations: t + dμ-

We present calculations of the cross-sections for elastic as well as for muon transfer in t + dμ^- collisions below the tμ^-(n = 2) threshold. The appropriate mass-scaled Jacobi coordinates are used in the direct and rearrangement channels. The K-matrix elements are obtained from the solution of multichannel Faddeev equations in the configuration space formulation. A bipolar expansion and spline representation are used in the numerical solution of the modified Faddeev equations. This revised version was published online in August 2006 with corrections to the Cover Date.