qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

Direct generation of optical vortices

A detailed scheme is established for the direct generation of optical vortices, signifying light endowed with orbital angular momentum. In contrast to common techniques based on the tailored conversion of the wave front in a conventional beam, this method provides for the direct spontaneous emission of photons with the requisite field structure. This form of optical emission results directly from the electronic relaxation of a delocalized exciton state that is supported by a ringlike array of three or more nanoscale chromophores. An analysis of the conditions leads to a general formulation revealing a requirement for the array structure to adhere to one of a restricted set of permissible symmetry groups. It is shown that the coupling between chromophores within each array leads to an energy level splitting of the exciton structure, thus providing for a specific linking of exciton phase and emission wavelength. For emission, arrays conforming to one of the given point-group families’ doubly degenerate excitons exhibit the specific phase characteristics necessary to support vortex emission. The highest order of exciton symmetry, corresponding to the maximum magnitude of electronic orbital angular momentum supported by the ring, provides for the most favored emission. The phase properties of the emission produced by the relaxation of such excitons are exhibited on plots which reveal the azimuthal phase progression around the ring, consistent with vortex emission. It is proven that emission of this kind produces electromagnetic fields that map with complete fidelity onto the phase structure of a Laguerre-Gaussian optical mode with the corresponding topological charge. The prospect of direct generation paves the way for practicable devices that need no longer rely on the modification of a conventional laser beam by a secondary optical element. Moreover, these principles hold promise for the development of a vortex laser, also based on nanoscale exciton decay, enabling the production of coherent radiation with a tailor-made helical wave front

Charge Carrier Extraction by Linearly Increasing Voltage:Analytic framework and ambipolar transients

Up to now the basic theoretical description of charge extraction by linearly increasing voltage (CELIV) is solved for a low conductivity approximation only. Here we present the full analytical solution, thus generalize the theoretical framework for this method. We compare the analytical solution and the approximated theory, showing that especially for typical organic solar cell materials the latter approach has a very limited validity. Photo-CELIV measurements on poly(3-hexyl thiophene-2,5-diyl):[6,6]-phenyl-C61 butyric acid methyl ester based solar cells were then evaluated by fitting the current transients to the analytical solution. We found that the fit results are in a very good agreement with the experimental observations, if ambipolar transport is taken into account, the origin of which we will discuss. Furthermore we present parametric equations for the mobility and the charge carrier density, which can be applied over the entire experimental range of parameters.Comment: 8 pages, 5 figure

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

Laser-controlled fluorescence in two-level systems

The ability to modify the character of fluorescent emission by a laser-controlled, optically nonlinear process has recently been shown theoretically feasible, and several possible applications have already been identified. In operation, a pulse of off-resonant probe laser beam, of sufficient intensity, is applied to a system exhibiting fluorescence, during the interval of excited- state decay following the initial excitation. The result is a rate of decay that can be controllably modified, the associated changes in fluorescence behavior affording new, chemically specific information. In this paper, a two-level emission model is employed in the further analysis of this all-optical process; the results should prove especially relevant to the analysis and imaging of physical systems employing fluorescent markers, these ranging from quantum dots to green fluorescence protein. Expressions are presented for the laser-controlled fluorescence anisotropy exhibited by samples in which the fluorophores are randomly oriented. It is also shown that, in systems with suitably configured electronic levels and symmetry properties, fluorescence emission can be produced from energy levels that would normally decay nonradiatively. © 2010 American Chemical Society

Inomogeneous Quantum Groups as Symmetries of Phonons

The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from the quantum group structure. Inhomogeneous quantum groups are thus proposed as kinematical invariance of discrete systems.Comment: 5 pags. 0 fig

Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure

Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials

Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric 3-particle Ruijsenaars model (relativistic generalization of Calogero-Moser-Sutherland model). In the quantum case, an integral operator M is constructed from the Askey-Wilson contour integral. The operator M transforms the eigenfunctions of the commuting Hamiltonians (Macdonald polynomials for the root sytem A2) into the factorized form S(y1)S(y2) where S(y) is a Laurent polynomial of one variable expressed in terms of the 3phi2(y) basic hypergeometric series. The inversion of M produces a new integral representation for the A2 Macdonald polynomials. We also present some results and conjectures for general n-particle case.Comment: 31 pages, latex, no figures, Proposition 12 correcte

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Optical angular momentum: Multipole transitions and photonics

The premise that multipolar decay should produce photons uniquely imprinted with a measurably corresponding angular momentum is shown in general to be untrue. To assume a one-to-one correlation between the transition multipoles involved in source decay and detector excitation is to impose a generally unsupportable one-to-one correlation between the multipolar form of emission transition and a multipolar character for the detected field. It is specifically proven impossible to determine without ambiguity, by use of any conventional detector, and for any photon emitted through the nondipolar decay of an atomic excited state, a unique multipolar character for the transition associated with its generation. Consistent with the angular quantum uncertainty principle, removal of a detector from the immediate vicinity of the source produces a decreasing angular uncertainty in photon propagation direction, reflected in an increasing range of integer values for the measured angular momentum. In such a context it follows that when the decay of an electronic excited state occurs by an electric quadrupolar transition, for example, any assumption that the radiation so produced is conveyed in the form of “quadrupole photons” is experimentally unverifiable. The results of the general proof based on irreducible tensor analysis invite experimental verification, and they signify certain limitations on quantum optical data transmission