426 research outputs found
Q-systems, Heaps, Paths and Cluster Positivity
We consider the cluster algebra associated to the -system for as a
tool for relating -system solutions to all possible sets of initial data. We
show that the conserved quantities of the -system are partition functions
for hard particles on particular target graphs with weights, which are
determined by the choice of initial data. This allows us to interpret the
simplest solutions of the Q-system as generating functions for Viennot's heaps
on these target graphs, and equivalently as generating functions of weighted
paths on suitable dual target graphs. The generating functions take the form of
finite continued fractions. In this setting, the cluster mutations correspond
to local rearrangements of the fractions which leave their final value
unchanged. Finally, the general solutions of the -system are interpreted as
partition functions for strongly non-intersecting families of lattice paths on
target lattices. This expresses all cluster variables as manifestly positive
Laurent polynomials of any initial data, thus proving the cluster positivity
conjecture for the -system. We also give an alternative formulation in
terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure
Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k
Using a form factor approach, we define and compute the character of the
fusion product of rectangular representations of \hat{su}(r+1). This character
decomposes into a sum of characters of irreducible representations, but with
q-dependent coefficients. We identify these coefficients as (generalized)
Kostka polynomials. Using this result, we obtain a formula for the characters
of arbitrary integrable highest-weight representations of \hat{su}(r+1) in
terms of the fermionic characters of the rectangular highest weight
representations.Comment: 21 pages; minor changes, typos correcte
The Many Faces of a Character
We prove an identity between three infinite families of polynomials which are
defined in terms of `bosonic', `fermionic', and `one-dimensional configuration'
sums. In the limit where the polynomials become infinite series, they give
different-looking expressions for the characters of the two integrable
representations of the affine algebra at level one. We conjecture yet
another fermionic sum representation for the polynomials which is constructed
directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9
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
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
Light Induced Increase of Electron Diffusion Length in a p n Junction Type CH3NH3PbBr3 Perovskite Solar Cell
High band gap, high open circuit voltage solar cells with methylammonium lead tribromide MAPbBr3 perovskite absorbers are of interest for spectral splitting and photoelectrochemical applications, because of their good performance and ease of processing. The physical origin of high performance in these and similar perovskite based devices remains only partially understood. Using cross sectional electron beaminduced current EBIC measurements, we find an increase in carrier diffusion length in MAPbBr3 Cl based solar cells upon low intensity a few percent of 1 sun intensity blue laser illumination. Comparing dark and illuminated conditions, the minority carrier electron diffusion length increases about 3.5 times from Ln 100 50 nm to 360 22 nm. The EBIC cross section profile indicates a p amp; 8722;n structure between the n FTO TiO2 and p perovskite, rather than the p amp; 8722;i amp; 8722;n structure, reported for the iodide derivative. On the basis of the variation in space charge region width with varying bias, measured by EBIC and capacitance amp; 8722;voltage measurements, we estimate the net doping concentration in MAPbBr3 Cl to be 3 amp; 8722;6 1017 cm amp; 8722;
Spinons and parafermions in fermion cosets
We introduce a set of gauge invariant fermion fields in fermionic coset
models and show that they play a very central role in the description of
several Conformal Field Theories (CFT's). In particular we discuss the explicit
realization of primaries and their OPE in unitary minimal models, parafermion
fields in CFT's and that of spinon fields in
Wess-Zumino-Witten models (WZW) theories. The higher level case () will be
briefly discussed. Possible applications to QHE systems and spin-ladder systems
are addressed.Comment: 6 pages, Latex file. Invited talk at International Seminar dedicated
to the memory of D.V.Volkov, Kharkov, January 5-7, 199
Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
We present fermionic sum representations of the characters
of the minimal models for all relatively prime
integers for some allowed values of and . Our starting point is
binomial (q-binomial) identities derived from a truncation of the state
counting equations of the XXZ spin chain of anisotropy
. We use the Takahashi-Suzuki method to express
the allowed values of (and ) in terms of the continued fraction
decomposition of (and ) where stands for
the fractional part of These values are, in fact, the dimensions of the
hermitian irreducible representations of (and )
with (and We also establish the duality relation 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
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
Quasi-particles in Fractional Quantum Hall Effect Edge Theories
We propose a quasi-particle formulation of effective edge theories for the
fractional quantum Hall effect. For the edge of a Laughlin state with filling
fraction \nu=1/m, our fundamental quasi-particles are edge electrons of charge
-e and edge quasi-holes of charge +e/m. These quasi-particles satisfy exclusion
statistics in the sense of Haldane. We exploit algebraic properties of edge
electrons to derive a kinetic equation for charge transport between a \nu=1/m
fractional quantum Hall edge and a normal metal. We also analyze alternative
`Boltzmann' equations that are directly based on the exclusion statistics
properties of edge quasi-particles. Generalizations to more general filling
fractions (Jain series) are briefly discussed.Comment: 20 pages, 2 eps figures, revtex, references updated, Phys. Rev. B in
pres
Exact conserved quantities on the cylinder I: conformal case
The nonlinear integral equations describing the spectra of the left and right
(continuous) quantum KdV equations on the cylinder are derived from integrable
lattice field theories, which turn out to allow the Bethe Ansatz equations of a
twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear
integral equation of the twisted continuous spin chain is found. The
diagonalization of the transfer matrix is performed. The vacua sector is
analysed in detail detecting the primary states of the minimal conformal models
and giving integral expressions for the eigenvalues of the transfer matrix.
Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and
Zamolodchikov is realised. General expressions for the eigenvalues of the
infinite-dimensional abelian algebra of local integrals of motion are given and
explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe
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