Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

A study of the nuclear-medium influence on neutral-strange-particle production in deep-inelastic neutrino scattering

The influence of nuclear effects on the production of neutral strange particles (V ⁰) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V ⁰ particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π⁻ mesons, . It is shown that the multiplicity gain of V ⁰ particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.     

Representations of \mathcal{U}_q (sl(3)) at roots of 1 (In the restricted specialisation)

Irreducible representations of at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra not to be completely diagonalised. Some irreducible representations of indeed contain indecomposable -modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation.     

A static cosmological model in Einstein-Cartan theory

A static cosmological model in the Einstein-Cartan theory based on Lyra's modified Riemannian geometry is proposed. We assume that the spins of the individual particles composng the fluid are all aligned in the radial direction and observe the very interesting fact that if spin is there in this static Einstein universe, it should be constant and it can be given in terms of central density ₀ as . The geometry and properties of the model are discussed.     

Level structure of149Nd. The decay of149Pr

The decay of¹⁴⁹Pr (T _1/2=2.2 min) has been studied using the two fission product separators JOSEF and LOHENGRIN to produce the¹⁴⁹Pr nucleus. A level scheme for¹⁴⁹Nd has been established. Theβ-branching and logft values for the excited levels were deduced from the analysis ofγ-intensity balances. Furthermore, the spins and parities for most of the excited states observed were obtained from the comparison between the present work, the neutron capture results and the pick-up reactions. The positive parity levels have been described with the Nilsson model with Coriolis andΔN=2 interactions included. The properties of the negative parity states cannot be explained as easily; however, it has been attempted to extract the structure of the ground state \((I^\pi = \tfrac{5}{2}^ - )\) and the first excited states \((I^\pi = \tfrac{7}{2}^ - and\tfrac{3}{2}^ - )\) .     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Measurement of the mass and the width of the W boson at LEP

The mass and the total decay width of the W boson are measured with the L3 detector at the LEP e⁺e^– collider using W-boson pairs produced in 0.7 fb^–1 of data collected at centre-of-mass energies between 161 and 209 GeV. Combining semi-leptonic and fully-hadronic final states, the mass and the width of the W boson are determined to be

On a few new quantization recipes using \mathcal{P}\mathcal{T}-symmetry

A review of a few recent developments in our analysis and applications of the coupled-channel version of the formalism of -symmetric quantum mechanics is given.     

Comparative analysis of real and \mathcal{P}\mathcal{T}-symmetric Scarf potentials

The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle the two potentials separately both in the conventional Hermitian and in the -symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy eigenvalues. Several main differences between the -symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number, the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of symmetry and the non- orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the corresponding Hermitian systems are also pointed out.     

Demixing in Isotropic Binary Mixtures of Rodlike Macromolecules

A binary mixture of long rigid rods of diameters D _i and lengths L _i (i=1, 2) may demix into two isotropic phases, and we give necessary conditions on the molecular size parameters for this transition to exist. These conditions imply that the two diameters must be sufficiently unequal, D ₂/D ₁>( + )², or D ₂/D ₁<( + )², while the length ratio is limited to an interval f _–(D ₂/D ₁)<L ₂/L ₁<f ₊(D ₂/D ₁). The functions f _± are given explicitly.     

Diquark Model for J/ψ Baryonic Decays

The baryonic decays of J/ provide a new way to study the internal structure of baryons. We apply a simple diquark model to the calculation of the decay cross-sections for the reactions J/ , N^*(1440), ^*N^*, and ⁰⁰. The results are different from those given by the ordinary constituent quark model. Hence these reactions may provide a new check of two different pictures for the baryons.     

Tunneling Across an Inhomogeneous Delta-Barrier

The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy (where 0$$ " align="middle" border="0"> and 0$$ " align="middle" border="0"> are two constants). In particular, the perpendicular incidence of an electron with a given value of the wave vector is considered. The electron is forward-scattered into the region behind the barrier (region 2: 0$$ " align="middle" border="0"> ), i. e. the wave function is composed of plane waves with all wave vectors such that and \left. 0 \right)} $$ " align="middle" border="0"> ) (where ). Therefore, if 0$$ " align="middle" border="0"> , the wave function of the electron is represented as , where . An approximate formula is derived for the amplitude . The authors pay a special attention to the flow density and calculate this function in two cases: 1. for the plane and 2. for high values of is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier.     

On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

Induced representations of the two-parameter Jordanian quantum algebra

We construct induced infinite-dimensional representations of the two-parameter quantum algebraUg,h(gl(2)) which is in duality with the deformationGLg,h(2). The representations depend on two representation parameters, but split into one-parameter representations of a one-generator central subalgebra and the three-generator Jordanian quantum subalgebraU (sl(2)), =g + h. The representations of the latter can be mapped to representations in one complex variable, which give anew deformation of the standard one-parameter vector-field realization ofsl(2). These infinite-dimensional representations are reducible for some values of the representation parameters, and then we obtain canonically the finite-dimensional representations ofU (sl(2)). Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Permanent address of V.K.D.     

Double quantization on the coadjoint representation of sl(n)

For we construct a two parametric -invariant family of algebras, , that is a quantization of the function algebra on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric -invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on .     

Dynamics of Alternating Spin Chains

We consider the dimerised spin- isotropic XY chain in a transverse field and study the xx and zz dynamic structure factors for different values of the Hamiltonian parameters and temperature.     

Minimal Model Fusion Rules From 2-Groups

The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group in the following manner. There is a partition into disjoint subsets and a bijection between and the sectors of the (p,q)-minimal model such that the fusion rules correspond to where .     

BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings

Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases, ₂ (the Virasoro string) and ₃ (the string).