33,191 research outputs found
Integrable Combinatorics
We review various combinatorial problems with underlying classical or quantum
integrable structures. (Plenary talk given at the International Congress of
Mathematical Physics, Aalborg, Denmark, August 10, 2012.)Comment: 21 pages, 16 figures, proceedings of ICMP1
Truncated determinants and the refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics
related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S.,
Nara, Japan.Comment: 25 pages, 8 figure
A refined Razumov-Stroganov conjecture II
We extend a previous conjecture [cond-mat/0407477] relating the
Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to
refined numbers of alternating sign matrices. By considering the O(1) loop
model on a semi-infinite cylinder with dislocations, we obtain the generating
function for alternating sign matrices with prescribed positions of 1's on
their top and bottom rows. This seems to indicate a deep correspondence between
observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf
macro
Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry
It is proven by explicit construction that regularization by dimensional
reduction can be formulated in a mathematically consistent way. In this
formulation the quantum action principle is shown to hold. This provides an
intuitive and elegant relation between the D-dimensional Lagrangian and Ward or
Slavnov-Taylor identities, and it can be used in particular to study to what
extent dimensional reduction preserves supersymmetry. We give several examples
of previously unchecked cases.Comment: 19 pages, 4 figures; minor modifications, published in JHE
Dynamical approach to chains of scatterers
Linear chains of quantum scatterers are studied in the process of
lengthening, which is treated and analysed as a discrete dynamical system
defined over the manifold of scattering matrices. Elementary properties of such
dynamics relate the transport through the chain to the spectral properties of
individual scatterers. For a single-scattering channel case some new light is
shed on known transport properties of disordered and noisy chains, whereas
translationally invariant case can be studied analytically in terms of a simple
deterministic dynamical map. The many-channel case was studied numerically by
examining the statistical properties of scatterers that correspond to a certain
type of transport of the chain i.e. ballistic or (partially) localised.Comment: 16 pages, 7 figure
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