14,478 research outputs found
Algebraic representation of correlation functions in integrable spin chains
Taking the XXZ chain as the main example, we give a review of an algebraic
representation of correlation functions in integrable spin chains obtained
recently. We rewrite the previous formulas in a form which works equally well
for the physically interesting homogeneous chains. We discuss also the case of
quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur
A recursion formula for the correlation functions of an inhomogeneous XXX model
A new recursion formula is presented for the correlation functions of the
integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators
involving n consecutive lattice sites to those with n-1 and n-2 sites. In a
series of papers by V. Korepin and two of the present authors, it was
discovered that the correlators have a certain specific structure as functions
of the inhomogeneity parameters. Our formula allows for a direct proof of this
structure, as well as an exact description of the rational functions which has
been left undetermined in the previous works.Comment: 37 pages, 1 figure, Proof of Lemma 4.8 modifie
Form factors of descendant operators: Free field construction and reflection relations
The free field representation for form factors in the sinh-Gordon model and
the sine-Gordon model in the breather sector is modified to describe the form
factors of descendant operators, which are obtained from the exponential ones,
\e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra
associated to the field . As a check of the validity of the
construction we count the numbers of operators defined by the form factors at
each level in each chiral sector. Another check is related to the so called
reflection relations, which identify in the breather sector the descendants of
the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi}
for generic values of . We prove the operators defined by the obtained
families of form factors to satisfy such reflection relations. A generalization
of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor
corrections; v4,v5: misprints corrected; v6: minor mistake correcte
Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
Starting from Rodrigues formula we present a general construction of raising
and lowering operators for orthogonal polynomials of continuous and discrete
variable on uniform lattice. In order to have these operators mutually adjoint
we introduce orthonormal functions with respect to the scalar product of unit
weight. Using the Infeld-Hull factorization method, we generate from the
raising and lowering operators the second order self-adjoint
differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission
Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice
We complete the construction of raising and lowering operators, given in a
previous work, for the orthogonal polynomials of hypergeometric type on
non-homogeneous lattice, and extend these operators to the generalized
orthogonal polynomials, namely, those difference of orthogonal polynomials that
satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org
Bimaximal Neutrino Mixing with Discrete Flavour Symmetries
In view of the fact that the data on neutrino mixing are still compatible
with a situation where Bimaximal mixing is valid in first approximation and it
is then corrected by terms of order of the Cabibbo angle, we present examples
where these properties are naturally realized. The models are supersymmetric in
4-dimensions and based on the discrete non-Abelian flavour symmetry S4.Comment: 8 pages, 1 figure; contribution prepared for DISCRETE'10 - Symposium
on Prospects in the Physics of Discrete Symmetrie
Exact evaluation of density matrix elements for the Heisenberg chain
We have obtained all the density matrix elements on six lattice sites for the
spin-1/2 Heisenberg chain via the algebraic method based on the quantum
Knizhnik-Zamolodchikov equations. Several interesting correlation functions,
such as chiral correlation functions, dimer-dimer correlation functions, etc...
have been analytically evaluated. Furthermore we have calculated all the
eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a
result the exact von Neumann entropy for the reduced density matrix on six
lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author
Neutrino masses and mixing
Status of determination of the neutrino masses and mixing is formulated and
possible uncertainties, especially due to presence of the sterile neutrinos,
are discussed. The data hint an existence of special ``neutrino'' symmetries.
If not accidental these symmetries have profound implications and can
substantially change the unification program. The key issue on the way to
underlying physics is relations between quarks and leptons. The approximate
quark-lepton symmetry or universality can be reconciled with strongly different
patterns of masses and mixings due to nearly singular character of the mass
matrices or screening of the Dirac structures in the double see-saw mechanism.Comment: 11 pages, latex, iopams.sty, 3 figures. Invited talk given at
TAUP2005, September 10 - 14, 2005, Zaragoza, Spai
Hyperspherical harmonics with arbitrary arguments
The derivation scheme for hyperspherical harmonics (HSH) with arbitrary
arguments is proposed. It is demonstrated that HSH can be presented as the
product of HSH corresponding to spaces with lower dimensionality multiplied by
the orthogonal (Jacobi or Gegenbauer) polynomial. The relation of HSH to
quantum few-body problems is discussed. The explicit expressions for
orthonormal HSH in spaces with dimensions from 2 to 6 are given. The important
particular cases of four- and six-dimensional spaces are analyzed in detail and
explicit expressions for HSH are given for several choices of hyperangles. In
the six-dimensional space, HSH representing the kinetic energy operator
corresponding to i) the three-body problem in physical space and ii) four-body
planar problem are derived.Comment: 18 pages, 1 figur
- …