A summation formula for Macdonald polynomials

We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and $q$-Whittaker polynomials.Comment: 8 page

Matrix product formula for Macdonald polynomials

We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik--Zamolodchikov equations, which arise by considering representations of the Zamolodchikov--Faddeev and Yang--Baxter algebras in terms of $t$-deformed bosonic operators. These solutions form a basis of the ring of polynomials in $n$ variables, whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalisations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at $q=1$.Comment: 27 pages; typos corrected, references added and some better conventions adopted in v

Matrix product and sum rule for Macdonald polynomials

We present a new, explicit sum formula for symmetric Macdonald polynomials $P_\lambda$ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov--Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang--Baxter algebra. As a corollary, we find that the normalization of the stationary measure of the multi-species asymmetric exclusion process is a Macdonald polynomial with all variables set equal to one.Comment: 11 pages, extended abstract submission to FPSA

A Class of Exact Solutions of the Wheeler -- De Witt Equation

After carefully regularizing the Wheeler -- De Witt operator, which is the Hamiltonian operator of canonical quantum gravity, we find a class of exact solutions of the Wheeler -- De Witt equation.Comment: 9 pages, Latex, (one reference and one conclusion added, minor corrections in the formulae

Characterisation at infrared wavelengths of metamaterials formed by thin-film metallic split-ring resonator arrays on silicon

The infrared reflectance spectra at normal incidence for split-ring resonator arrays fabricated in thin films of three different metals on a silicon substrate are reported. The results are compared with a finite difference time domain simulation of the structures and a simple and novel equivalent-circuit method for the calculation of the first and second resonant wavelengths

Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler-Feynman absorber

The altered spontaneous emission of an emitter near an arbitrary body can be elucidated using an energy balance of the electromagnetic field. From a classical point of view it is trivial to show that the field scattered back from any body should alter the emission of the source. But it is not at all apparent that the total radiative and non-radiative decay in an arbitrary body can add to the vacuum decay rate of the emitter (i.e.) an increase of emission that is just as much as the body absorbs and radiates in all directions. This gives us an opportunity to revisit two other elegant classical ideas of the past, the optical theorem and the Wheeler-Feynman absorber theory of radiation. It also provides us alternative perspectives of Purcell effect and generalizes many of its manifestations, both enhancement and inhibition of emission. When the optical density of states of a body or a material is difficult to resolve (in a complex geometry or a highly inhomogeneous volume) such a generalization offers new directions to solutions.Comment: 18 pages, 2 figure

Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem

A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is treated in detail. Unlike standard quantum theory both quantum and classical measuring device can be accommodated by the present approach to solve the quantum measurement problemComment: 29 pages, 4 figure

Information gap for classical and quantum communication in a Schwarzschild spacetime

Communication between a free-falling observer and an observer hovering above the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise, which degrades communication channels. Ignoring time dilation, which affects all channels equally, we show that for bosonic communication using single and dual rail encoding the classical channel capacity reaches a finite value and the quantum coherent information tends to zero. We conclude that classical correlations still exist at infinite acceleration, whereas the quantum coherence is fully removed.Comment: 5 pages, 4 figure