The solution of the quantum A1A_1 T-system for arbitrary boundary

We solve the quantum version of the $A_1$ $T$-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum $A_1$ $Q$-system and generalize it to the fully non-commutative case. We give the relation between the quantum $T$-system and the quantum lattice Liouville equation, which is the quantized $Y$-system.Comment: 24 pages, 18 figure

Laughlin's wave functions, Coulomb gases and expansions of the discriminant

In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermodynamically equivalent spherical plasma. In a second part, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.Comment: 97 pages, using harvmac (with big option recommended) and epsf, 7 figures available upon request, Saclay preprint Spht 93/12

Rapid Serial Visual Presentation. Degradation of inferential reading comprehension as a function of speed

There is increasing interest in the readability of text presented on small digital screens. Designers have come up with novel text presentation methods, such as moving text from right to left, line-stepping, or showing successive text segments such as phrases or single words in a RSVP format. Comparative studies have indicated that RSVP is perhaps the best method of presenting text in a limited space. We tested the method using 209 participants divided into six groups. The groups included traditional reading, and RSVP reading at rates of 250, 300, 350, 400, and 450 wpm. No significant differences were found in comprehension for normal reading and RSVP reading at rates of 250, 300 and 350 wpm. However, higher rates produced significantly lower comprehension scores. It remains to be determined if, with additional practice and improved methods, good levels of reading comprehension at high rates can be achieved with RSV

Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric Transpose Complement Plane Partitions and related combinatorial objects

A Bijection between classes of Fully Packed Loops and Plane Partitions

It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b x c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions

Recent advances on physico-chemical characterization of passive films by EIS and differential admittance techniques

Thin Nb2O5 anodic films (20 nm thick) grown in phosphoric acid solution have been characterised by EIS and differential admittance study in a large range of potential and frequency. The overall electrical behaviour has been interpreted by means of the theory of amorphous semiconductor Schottky barrier in presence of a non-constant density of states (DOS). A comparison of DOS for films grown in different electrolytes is reported

The Svetitsky-Yaffe conjecture for the plaquette operator

According to the Svetitsky-Yaffe conjecture, a (d+1)-dimensional pure gauge theory undergoing a continuous deconfinement transition is in the same universality class as a d-dimensional statistical model with order parameter taking values in the center of the gauge group. We show that the plaquette operator of the gauge theory is mapped into the energy operator of the statistical model. For d=2, this identification allows us to use conformal field theory techniques to evaluate exactly the correlation functions of the plaquette operator at the critical point. In particular, we can evaluate exactly the plaquette expectation value in presence of static sources, which gives some new insight in the structure of the color flux tube in mesons and baryons.Comment: 8 pages, LaTeX file + three .eps figure

Physicochemical characterization of passive films on niobium by admittance and electrochemical impedance spectroscopy studies

An analysis of the electronic properties of amorphous semiconductor–electrolyte junction is reported for thin (Dox < 20 nm) passive film grown on Nb in acidic electrolyte. It will be shown that the theory of amorphous semiconductor–electrolyte junction (a-SC/El) both in the low band-bending and high band-bending regime is able to explain the admittance data of a-Nb2O5/El interface in a large range (10 Hz–10 kHz) of frequency and electrode potential values. A modelling of experimental EIS data at different potentials and in the frequency range of 0.1 Hz–100 kHz is presented based on the theory of amorphous semiconductor and compared with the results of the fitting of the admittance data obtained in a different experiment. Some preliminary insights on the possible dependence of the density of state (DOS) distribution on the mobile defects concentration and mechanism of growth of anodic film on valve metals are suggested

Nature of the Vacuum inside the Color Flux Tube

The interior of the color flux tube joining a quark pair can be probed by evaluating the correlator of pair of Polyakov loops in a vacuum modified by another Polyakov pair, in order to check the dual superconductivity conjecture which predicts a deconfined, hot core. We also point out that at the critical point of any 3D gauge theories with a continuous deconfining transition the Svetitsky-Yaffe conjecture provides us with an analytic expression of the Polyakov correlator as a function of the position of the probe inside the flux tube. Both these predictions are compared with numerical results in 3D Z2 gauge model finding complete agreement.Comment: 3 pages, Talk presented at LATTICE96(topology

Lie-Algebraic Characterization of 2D (Super-)Integrable Models

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is discussed. The super- symmetric case will be particularly enphasized. The fundamental examples will be outlined.Comment: 6 pages, LaTex, Talk given at the conference in memory of D.V. Volkov, Kharkhov, January 1997. To appear in the proceeding