Exceptional structure of the dilute A3_3 model: E8_8 and E7_7 Rogers--Ramanujan identities

The dilute A$_3$ lattice model in regime 2 is in the universality class of the Ising model in a magnetic field. Here we establish directly the existence of an E$_8$ structure in the dilute A$_3$ model in this regime by expressing the 1-dimensional configuration sums in terms of fermionic sums which explicitly involve the E$_8$ root system. In the thermodynamic limit, these polynomial identities yield a proof of the E$_8$ Rogers--Ramanujan identity recently conjectured by Kedem {\em et al}. The polynomial identities also apply to regime 3, which is obtained by transforming the modular parameter by $q\to 1/q$. In this case we find an A_1\times\mbox{E}_7 structure and prove a Rogers--Ramanujan identity of A_1\times\mbox{E}_7 type. Finally, in the critical $q\to 1$ limit, we give some intriguing expressions for the number of $L$-step paths on the A$_3$ Dynkin diagram with tadpoles in terms of the E$_8$ Cartan matrix. All our findings confirm the E$_8$ and E$_7$ structure of the dilute A$_3$ model found recently by means of the thermodynamic Bethe Ansatz.Comment: 9 pages, 1 postscript figur

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

AL 3 (BH 261): a new globular cluster in the Galaxy

AL~3 (BH 261), previously classified as a faint open cluster candidate, is shown to be a new globular cluster in the Milky Way, by means of B, V and I Color-Magnitude Diagrams. The main feature of AL~3 is a prominent blue extended Horizontal Branch. Its Color-Magnitude Diagrams match those of the intermediate metallicity cluster M~5. The cluster is projected in a rich bulge field, also contaminated by the disk main sequence. The globular cluster is located in the Galactic bulge at a distance from the Sun d$_{\odot}$ = 6.0$\pm$0.5 kpc. The reddening is E(B-V)=0.36$\pm$0.03 and the metallicity is estimated to be [Fe/H] $\approx$ -1.3$\pm$0.25. AL~3 is probably one of the least massive globular clusters of the Galaxy.Comment: 6 figures. Astrophysical Journal Letters, in pres

On two 10th order mock theta identities

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa

Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter and Forrester, we find proof of polynomial identities for finitizations of the Virasoro characters $\chi_{b,a}^{(r-1,r)}(q)$ as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers--Ramanujan type identities for the unitary minimal Virasoro characters, conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure

On the Form Factors of Relevant Operators and their Cluster Property

We compute the Form Factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous dimensions by means of Delfino--Simonetti--Cardy sum--rule and further confirmed by comparing some universal ratios of the nearby non--integrable quantum field theories with their independent numerical determination.Comment: Latex file, 35 pages with 5 Postscript figure