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Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points via Ginzburg–Landau Polynomials
Magnetization the gold the Pittsburgh landau lattice spin model the inversion temperature
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2014/12/19
The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landa...
Families of superintegrable Hamiltonians constructed from exceptional polynomials
Families of superintegrable Hamiltonians exceptional polynomials Mathematical Physics
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2012/6/19
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum t...
Efficiently Testing Sparse GF(2) Polynomials
Property testing GF(2) polynomials Sparse polynomials Randomized algorithms
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2012/12/3
We give the first algorithm that is both query-efficient and time-efficient for testing whether an unknown function f : {0, 1}n → {−1, 1} is an s-sparse
GF(2) polynomial versus -far from every...
Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials
Alexander Polynomial Invariants Chebyshev Polynomials Mathematical Physics
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2011/9/22
Abstract: The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. U...
Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
Spin-Singlet Quantum Hall States Jack Polynomials Prescribed Symmetry
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2011/10/8
Abstract: We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wave-functions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed...
Orthogonal polynomials in the normal matrix model with a cubic potential
Orthogonal polynomials the normal matrix model Classical Analysis and ODEs
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2011/7/27
Orthogonal polynomials in the normal matrix model with a cubic potential.
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs
Systems of Kowalevski type discriminantly separable polynomials quad-graphs
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2011/7/27
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs.
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
multiple Charlier polynomials non-Hermitian Hamiltonians algebraic model
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2011/7/26
Abstract: A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of mult...
The expansion in ultraspherical polynomials: a simple procedure for the fast computation of the ultraspherical coefficients
Ultraspherical expansions Gegenbauer coefficients Abel transform
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2011/7/28
Abstract: We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coeffic...
On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values
Fully Packed Loops configurations negative values Combinatorics
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2011/7/28
Abstract: In this article, we are interested in the enumeration of Fully Packed Loops configurations on a grid with a given noncrossing matching. These quantities also appear as the groundstate compon...
The "boson polynomials" of Gel'fand basis and the analytic expression of Wigner's coefficients with multiplicity for the canonical basis of unitary groups
Gel'fand basis Wigner's coefficients canonical basis Representation Theory
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2011/7/26
Abstract: In this paper we present the generating function method for the derivation of bosons polynomials of Gel'fand basis and Wigner coefficients for the canonical basis of SU(n). We find a new ana...
Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials
quantum mechanics supersymmetry orthogonal polynomials
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2011/7/26
Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials.
Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement
Riemann--Hilbert problems matrix orthogonal polynomials discrete matrix equations singularity confinement
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2011/7/27
Abstract: In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the cor...
Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
Parafermionic polynomials Selberg integrals
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2010/12/23
In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In par...
Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States
Deciding Unitary Equivalence Matrix Polynomials Sets of Bipartite Quantum States
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2010/10/29
In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebr...