Realizations ofU q(su(1, 1)) by deformed quantum harmonic oscillator algebras and associated deformed Heisenberg algebras

Forsu(1, 1)-symmetric Hamiltonians of quantum mechanical systems (e.g. single-mode quantum harmonic oscillator, radial Schrödinger equation for Coulomb problem or isotropic quantum harmonic oscillator, etc.), the Heisenberg algebra of phase-space variables in two dimensions satisfy the bilinear commutation relation [ip,x]=1 (in normal units). Also there are different realizations ofsu(1, 1) by the generators of quantum harmonic oscillator algebra. We seek here the forms of deformed Heisenberg algebras (bilinear in deformedx and ip) associated with deformedsu(1, 1)-symmetric Hamiltonians. These forms are not unique in contrast to the undeformed case; and these forms are obtained here by considering different realizations of the deformedsu(1, 1) algebra by deformed oscillator algebras (satisfying different bilinear relations in deformed creation and annihilation operators), and then imposing different conditions (e.g. the deformed Heisenberg algebra of the form of the undeformed one, the form of realizations of the deformedsu(1, 1) algebra by deformed phase-space variables being the same as that ofsu(1, 1) algebra by undeformed phase-space variables, etc.), assuming linear relations between deformed phase-space variables and deformed creation-annihilation operators (as it is done in the undeformed case), we get different Heisenberg algebras. These facts are revealed in the case of a two-body Calogero model in its centre of mass frame (and for no other integrable systems in one-dimension having potential of the formV(x _i ? x_j).     

The <Emphasis Type="Italic">q</Emphasis>-boson-fermion realizations of the quantum superalgebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">osp</Emphasis>(1/2))

We show that our construction of realizations for algebras and quantum algebras can be generalized to quantum superalgebras too. We studyan example of quantum superalgebra U _q (osp(1/2)) and give the boson-fermion realization with respect to one pair of q-boson operators and one pair of fermions.     

Dynamical algebras for Pöschl-Teller Hamiltonian hierarchies

The dynamical algebras of the trigonometric and hyperbolic symmetric Pöschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.     

Canonical realizations of classical lie algebras

We construct sets of canonical realizations for all classical Lie algebras (A _n ,B _n ,C _n ,D _n ). These realizations depend ond parameters,d=1, 2, 3,...,n; all Casimir operators are realized by multiples of identity. For most of the real forms of these algebras we give sets of realizations which are, moreover, in well-defined sense skew-Hermitian. Further we study extremal cases of the presented realizations. The realizations with minimal numbers of canonical pairs are discussed from the point of view of general results concerning minimal realizations. On the other hand, a connection is found between our maximal realizations ofA _n and the Gel'fand-Kirillov Conjecture.The authors would like to thank Prof. A.Uhlmann for his kind interest in this work. They are very grateful to Prof. A. A.Kirillov and Prof. D. P.Zhelobenko for helpful discussions and to Prof. J.Dixmier for his informative letter concerning the problem mentioned in Sect. 5.One of the authors (W. L.) thanks Prof. I.Úlehla for the hospitality at the Nuclear Center of the Charles University, Praha.     

Twist of Lie algebras by a rank-3 subalgebra

A new nonstandard deformation of all types of classical Lie algebras is constructed by means of twisting based on a six-dimensional subalgebra. This is an extension of extended twists introduced by Kulish et al. It is also shown that the new nonstandard so(3, 2) has a close connection with the symmetry of a discrete analog of the Klein-Gordon equation in (1+2) spacetime.     

A New Current Algebra and the Reflection Equation

We establish an explicit algebra isomorphism between the quantum reflection algebra for the U_q([^(sl₂)]) R{U_q(\widehat{sl_2}) R}-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal algebras (q-Onsager).     

On new conformal field theories with affine fusion rules

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have extended W algebras which are close analogues of affine algebras. Exact character formulae are given, and the realizations are shown to be full-fledged unitary conformal field theories.     

Classification and Realizations of Type III Factor Representations of Cuntz–Krieger Algebras Associated with Quasi-Free States

We completely classify type III factor representations of Cuntz–Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type II₁ factor representations are used in these realizations.      

Carrier collection in a semiconductor quantum well

Data are presented showing that a GaAs quantum well, sandwiched between two epitaxial Al_xGa_1-xAs(x ～ 0.4) confining layers, loses its effectiveness as a collector of excess carriers and as a source of recombination radiation for well dimensions L_z < 100 Å. It is shown that this behavior is expected because of the difficulty in scattering carriers to the bottom of the quantum well as L_z → l_p, the path length for scattering (LO phonon).     

A new derivation of the Marshalek-Okubo realization of the shell-model algebraso(2v+1) for even and odd systems withv single-particle levels

In recent years, the method for unitarizing nonunitary Dyson boson realizations of shellmodel algebras has been both generalized and substantially simplified through the introduction of overtly group-theoretical methods. In this paper, these methods are applied to the boson-odd-particle realization of the algebra SO(2v+1) forv single-particle levels, adapted to the group chain SO(2v+ l)?SO(2v)?U(v), which Marshalek first derived by brute force summation of a Taylor expansion and later Okubo by a largely algebraic technique.     

多模双参数变形相干态

借助一个满足量子Heisenberg-Weyl代数(H-W_q,s代数)的多模算符,给出了量子代数SU(2)_q,s和SU(1,1)_q,s的k(k≥2)模实现,并构造了相应的相干态.     

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

With the aid of the macroscopic dielectric continuum and Loudon’s uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/A_l0.15Ga_0.85N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k _z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k _z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.     

Topologically appropriate coordinates for (Vzz, η) joint probability distributions

Inhomogeneous broadening (IHB) of hyperfine interactions in materials arises from a distribution of electric field gradients (EFGs) due to randomly distributed defects contributing non-uniformly to the EFG at probe sites. Hyperfine experiments reflect the inhomogeneous distribution of defects through the joint probability distribution function (PDF) of V_zz and η determined by the defect concentration, crystal structure, and defect sites in the crystal. Czjzek showed how to choose coordinates in the (V_zz, η) plane that are consistent with the physical constraints and ordering convention for these EFG parameters. Here we show how to transform to a new set of coordinates that decreases the distortion inherent in Czjzek’s representation. These new coordinates allow one to express the joint PDF for random distributions of defects in a form reasonably approximated by the product of two independent marginal distributions. This paper focuses on these topologically appropriate coordinates, with simple examples drawn from Czjzek’s work and from our simulations of point defects in cubic lattices as well as random amorphous distributions of defects. Detailed simulations have been carried out for IHB in cubic structures and point charge models relevant to perturbed angular correlation (PAC) experiments.     

The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

State-of-the-art airborne lidar data of passive scalars have shown that the spatial stratification of the atmosphere is scaling: the vertical extent (Δz) of structures is typically ≈Δx^H_z where Δx is the horizontal extent and H_z is a stratification exponent. Assuming horizontal isotropy, the volumes of the structures therefore vary as ΔxΔxΔx^H_z=Δx^D_s where the “elliptical dimension” D_s characterizes the rate at which the volumes of typical non-intermittent structures vary with scale. Work on vertical cross-sections has shown that 2+H_z=2.55±0.02 (close to the theoretical prediction 23/9).In this paper we extend these (x, z) analyses to (z, t). In the absence of overall advection, the lifetime Δt of a structure of size Δx varies as Δx^H_t with H_t=2/3 so that the overall space-time dimension is D_st=29/9=3.22…. However, horizontal and vertical advection lead to new exponents: we argue that the temporal stratification exponent H_t≈1 or ≈0.7 depending on the relative importance of horizontal versus vertical advection velocities. We empirically test these space-time predictions using vertical-time (z, t) cross-sections using passive scalar surrogates (aerosol backscatter ratios from lidar) at ∼3 m resolution in the vertical, 0.5-30 s in time and spanning 3-4 orders of magnitude in scale as well as new analyses of vertical (x, z) cross-sections (spanning over 3 orders of magnitude in both x, z directions). In order to test the theory for density fluctuations at arbitrary displacements in (Δz, Δt) and (Δx, Δz) spaces, we developed and applied a new Anisotropic Scaling Analysis Technique (ASAT) based on nonlinear coordinate transformations. Applying this and other analyses to data spanning more than 3 orders of magnitude of space-time scales we determined the anisotropic scaling of space-time finding the empirical value D_st=3.13±0.16. The analyses also show that both cirrus clouds and aerosols had very similar space-time scaling properties. We point out that this model is compatible with (nonlinear) “turbulence” waves, hence potentially explaining the observed atmospheric structures.     

Verification of <Emphasis Type="Italic">z</Emphasis> scaling at RHIC and Tevatron

The concept of z scaling reflecting the general features of high-p _T particle production is reviewed. Properties of data z presentation are discussed. New data on high-p _T particle spectra obtained at the RHIC and Tevatron are analyzed in the framework of z presentation. It was shown that these experimental data confirm z scaling. The change in the anomalous fractal dimensions of colliding objects (“δ jump”) is considered as a signature of new physics. The kinematic ranges preferable for searching for z-scaling violation are established.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

Surface and bulk plasmons in interaction with quantum well inter- and intra-subband plasmons

The collective oscillations of a 2D quantum well electron plasma embedded in a semi-infinite host plasma medium (at a distancez₀from the surface) are analyzed here, based on an explicit inversion of the joint dielectric function of the combined system in position representation in closed form. The coupling ofsurfaceand bulk plasmons of the host medium withintersubband and intrasubband plasmons of the quantum well, and the dependence of the coupled modes onz₀are discussed.