1,320 research outputs found
A Q-operator for the twisted XXX model
Taking the isotropic limit in a recent representation theoretic construction
of Baxter's Q-operators for the XXZ model with quasi-periodic boundary
conditions we obtain new results for the XXX model. We show that quasi-periodic
boundary conditions are needed to ensure convergence of the Q-operator
construction and derive a quantum Wronskian relation which implies two
different sets of Bethe ansatz equations, one above the other below the
"equator" of total spin zero. We discuss the limit to periodic boundary
conditions at the end and explain how this construction might be useful in the
context of correlation functions on the infinite lattice. We also identify a
special subclass of solutions to the quantum Wronskian for chains up to a
length of 10 sites and possibly higher.Comment: 19 page
PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to
be quasi-Hermitian for special values of the boundary parameters. This is
proved by explicit construction of a new inner product employing a
"quasi-fermion" algebra in momentum space where creation and annihilation
operators are not related via Hermitian conjugation. For a special example,
when the boundary fields lie on the imaginary axis, we show the spectral
equivalence of the quasi-Hermitian XX spin-chain with a non-local fermion
model, where long range hopping of the particles occurs as the non-Hermitian
boundary fields increase in strength. The corresponding Hamiltonian
interpolates between the open XX and the quantum group invariant XXZ model at
the free fermion point. For an even number of sites the former is known to be
related to a CFT with central charge c=1, while the latter has been connected
to a logarithmic CFT with central charge c=-2. We discuss the underlying
algebraic structures and show that for an odd number of sites the superalgebra
symmetry U(gl(1|1)) can be extended from the unit circle along the imaginary
axis. We relate the vanishing of one of its central elements to the appearance
of Jordan blocks in the Hamiltonian.Comment: 37 pages, 5 figure
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
The construction of auxiliary matrices for the six-vertex model at a root of
unity is investigated from a quantum group theoretic point of view. Employing
the concept of intertwiners associated with the quantum loop algebra
at a three parameter family of auxiliary matrices
is constructed. The elements of this family satisfy a functional relation with
the transfer matrix allowing one to solve the eigenvalue problem of the model
and to derive the Bethe ansatz equations. This functional relation is obtained
from the decomposition of a tensor product of evaluation representations and
involves auxiliary matrices with different parameters. Because of this
dependence on additional parameters the auxiliary matrices break in general the
finite symmetries of the six-vertex model, such as spin-reversal or spin
conservation. More importantly, they also lift the extra degeneracies of the
transfer matrix due to the loop symmetry present at rational coupling values.
The extra parameters in the auxiliary matrices are shown to be directly related
to the elements in the enlarged center of the quantum loop algebra
at . This connection provides a geometric
interpretation of the enhanced symmetry of the six-vertex model at rational
coupling. The parameters labelling the auxiliary matrices can be interpreted as
coordinates on a three-dimensional complex hypersurface which remains invariant
under the action of an infinite-dimensional group of analytic transformations,
called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references
adde
Atmospheric neutrons
Contributions to fast neutron measurements in the atmosphere are outlined. The results of a calculation to determine the production, distribution and final disappearance of atmospheric neutrons over the entire spectrum are presented. An attempt is made to answer questions that relate to processes such as neutron escape from the atmosphere and C-14 production. In addition, since variations of secondary neutrons can be related to variations in the primary radiation, comment on the modulation of both radiation components is made
The functional organization of descending sensory-motor pathways in Drosophila
In most animals, the brain controls the body via a set of descending neurons (DNs) that traverse the neck. DN activity activates, maintains or modulates locomotion and other behaviors. Individual DNs have been well-studied in species from insects to primates, but little is known about overall connectivity patterns across the DN population. We systematically investigated DN anatomy in Drosophila melanogaster and created over 100 transgenic lines targeting individual cell types. We identified roughly half of all Drosophila DNs and comprehensively map connectivity between sensory and motor neuropils in the brain and nerve cord, respectively. We find the nerve cord is a layered system of neuropils reflecting the flyâs capability for two largely independent means of locomotion -- walking and flight -- using distinct sets of appendages. Our results reveal the basic functional map of descending pathways in flies and provide tools for systematic interrogation of neural circuits
The Baxter's Q-operator for the W-algebra
The q-oscillator representation for the Borel subalgebra of the affine
symmetry is presented. By means of this q-oscillator
representation, we give the free field realizations of the Baxter's Q-operator
, for the W-algebra . We give the functional
relations of the - operators, including the higher-rank generalization of
the Baxter's - relation.Comment: LaTE
Attitudes towards the use and acceptance of eHealth technologies : a case study of older adults living with chronic pain and implications for rural healthcare
Acknowledgements The research described here is supported by the award made by the RCUK Digital Economy programme to the dot.rural Digital Economy Hub; award reference: EP/G066051/1. MCâs time writing the paper is funded by the Scottish Governmentâs Rural and Environmental Science and Analytical Services Division (RESAS) under Theme 8 âVibrant Rural Communitiesâ of the Food, Land and People Programme (2011â2016). MC is also an Honorary Research Fellow at the Division of Applied Health Sciences, University of Aberdeen. The input of other members of the TOPS research team, Alastair Mort, Fiona Williams, Sophie Corbett, Phil Wilson and Paul MacNamee who contributed to be wider study and discussed preliminary findings reported here with the authors of the paper is acknowledged. We acknowledge the feedback on earlier versions of this paper provided by members of the Trans-Atlantic Rural Research Network, especially Stefanie Doebler and Carmen Hubbard. We also thank Deb Roberts for her comments.Peer reviewedPublisher PD
On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
A class of pseudo-hermitian quantum system with an explicit form of the
positive-definite metric in the Hilbert space is presented. The general method
involves a realization of the basic canonical commutation relations defining
the quantum system in terms of operators those are hermitian with respect to a
pre-determined positive definite metric in the Hilbert space. Appropriate
combinations of these operators result in a large number of pseudo-hermitian
quantum systems admitting entirely real spectra and unitary time evolution. The
examples considered include simple harmonic oscillators with complex angular
frequencies, Stark(Zeeman) effect with complex electric(magnetic) field,
non-hermitian general quadratic form of N boson(fermion) operators, symmetric
and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian
Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of
Physics A(v3
- âŠ