360 research outputs found
Slavnov and Gaudin-Korepin Formulas for Models without Symmetry: the Twisted XXX Chain
We consider the XXX spin- Heisenberg chain on the circle with an
arbitrary twist. We characterize its spectral problem using the modified
algebraic Bethe anstaz and study the scalar product between the Bethe vector
and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the
model. Thus we provide a first example of such formulas for quantum integrable
models without symmetry characterized by an inhomogenous Baxter
T-Q equation
Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric -Matrix
We study quantum integrable models with GL(3) trigonometric -matrix and
solvable by the nested algebraic Bethe ansatz. Using the presentation of the
universal Bethe vectors in terms of projections of products of the currents of
the quantum affine algebra onto intersections of
different types of Borel subalgebras, we prove that the set of the nested Bethe
vectors is closed under the action of the elements of the monodromy matrix
Bethe vectors of GL(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. Different formulas are given for the Bethe vectors and the actions of
the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These
actions are relevant for the calculation of correlation functions and form
factors of local operators of the underlying quantum models.Comment: 22 pages, typos correcte
Form factors in SU(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. We obtain determinant representations for form factors of diagonal
entries of the monodromy matrix. This representation can be used for the
calculation of form factors and correlation functions of the XXX
SU(3)-invariant Heisenberg chain.Comment: 15 pages; typos correcte
Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
In this paper, we prove the off-shell equation satisfied by the transfer
matrix associated with the XXZ spin- chain on the segment with two
generic integrable boundaries acting on the Bethe vector. The essential step is
to prove that the expression of the action of a modified creation operator on
the Bethe vector has an off-shell structure which results in an inhomogeneous
term in the eigenvalues and Bethe equations of the corresponding transfer
matrix.Comment: V2 published version, 16 page
Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
The spectral problem of the Heisenberg XXZ spin- chain on the
segment is investigated within a modified algebraic Bethe ansatz framework. We
consider in this work the most general boundaries allowed by integrability. The
eigenvalues and the eigenvectors are obtained. They are characterised by a set
of Bethe roots with cardinality equal to , the length of the chain, and
which satisfies a set of Bethe equations with an additional term.Comment: V2 published versio
Highest coefficient of scalar products in SU(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. Scalar products of Bethe vectors in such models can be expressed in
terms of a bilinear combination of their highest coefficients. We obtain
various different representations for the highest coefficient in terms of sums
over partitions. We also obtain multiple integral representations for the
highest coefficient.Comment: 17 page
Reflection matrices for the vertex model
The graded reflection equation is investigated for the
vertex model. We have found four classes of diagonal
solutions and twelve classes of non-diagonal ones. The number of free
parameters for some solutions depends on the number of bosonic and fermionic
degrees of freedom considered.Comment: 30 page
Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in diamond anvil cell. Application to the stability study of AlPdMn
We report an innovative high pressure method combining the diamond anvil cell
device with the technique of picosecond ultrasonics. Such an approach allows to
accurately measure sound velocity and attenuation of solids and liquids under
pressure of tens of GPa, overcoming all the drawbacks of traditional
techniques. The power of this new experimental technique is demonstrated in
studies of lattice dynamics, stability domain and relaxation process in a
metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon
and argon. Application to the study of defect-induced lattice stability in
AlPdMn up to 30 GPa is proposed. The present work has potential for application
in areas ranging from fundamental problems in physics of solid and liquid
state, which in turn could be beneficial for various other scientific fields as
Earth and planetary science or material research
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