2,934 research outputs found
Onsager's algebra and partially orthogonal polynomials
The energy eigenvalues of the superintegrable chiral Potts model are
determined by the zeros of special polynomials which define finite
representations of Onsager's algebra. The polynomials determining the
low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they
satisfy 4-term recursion relations and so cannot form orthogonal sequences.
However, we show that they are closely related to Jacobi polynomials and
satisfy a special "partial orthogonality" with respect to a Jacobi weight
function.Comment: 8 pages, no figure
Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain
We study the excitation spectrum and the correlation functions of the Z_3-
chiral Potts model in the massive high-temperature phase using perturbation
expansions and numerical diagonalization. We are mainly interested in results
for general chiral angles but we consider also the superintegrable case. For
the parameter values considered, we find that the band structure of the low-
lying part of the excitation spectrum has the form expected from a
quasiparticle picture with two fundamental particles. Studying the N-dependence
of the spectrum, we confirm the stability of the second fundamental particle in
a limited range of the momentum, even when its energy becomes so high that it
lies very high up among the multiparticle scattering states. This is not a
phenomenon restricted to the superintegrable line. Calculating a
non-translationally invariant correlation function, we give evidence that it is
oscillating. Within our numerical accuracy we find a relation between the
oscillation length and the dip position of the momentum dispersion of the
lightest particle which seems to be quite independent of the chiral angles.Comment: 19 pages + 6 PostScript figures (LaTeX); BONN-TH-94-2
Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
A Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with
nondiagonal boundary terms has recently been proposed. Using a numerical
procedure developed by McCoy et al., we find significant evidence that this
solution can yield the complete set of eigenvalues for generic values of the
bulk and boundary parameters satisfying one linear relation. Moreover, our
results suggest that this solution is practical for investigating the ground
state of this model in the thermodynamic limit.Comment: 15 pages, LaTeX; amssymb, amsmath, no figures, 5 tables; v2 contains
an additional footnote and a "Note Added"; v3 contains an Addendu
Scaling of the von Neumann entropy across a finite temperature phase transition
The spectrum of the reduced density matrix and the temperature dependence of
the von Neumann entropy (VNE) are analytically obtained for a system of hard
core bosons on a complete graph which exhibits a phase transition to a
Bose-Einstein condensate at . It is demonstrated that the VNE undergoes
a crossover from purely logarithmic at T=0 to purely linear in block size
behaviour for . For intermediate temperatures, VNE is a sum of two
contributions which are identified as the classical (Gibbs) and the quantum
(due to entanglement) parts of the von Neumann entropy.Comment: 4 pages, 2 figure
Quantum Control Theory for State Transformations: Dark States and their Enlightenment
For many quantum information protocols such as state transfer, entanglement
transfer and entanglement generation, standard notions of controllability for
quantum systems are too strong. We introduce the weaker notion of accessible
pairs, and prove an upper bound on the achievable fidelity of a transformation
between a pair of states based on the symmetries of the system. A large class
of spin networks is presented for which this bound can be saturated. In this
context, we show how the inaccessible dark states for a given
excitation-preserving evolution can be calculated, and illustrate how some of
these can be accessed using extra catalytic excitations. This emphasises that
it is not sufficient for analyses of state transfer in spin networks to
restrict to the single excitation subspace. One class of symmetries in these
spin networks is exactly characterised in terms of the underlying graph
properties.Comment: 14 pages, 3 figures v3: rewritten for increased clarit
Comparison of vascular and respiratory effects of endothelin-1 in the pig
The haemodynamic and respiratory responses caused by i.v. administration of endothelin-1 (ET-1) (20–100 pmol/kg) were studied in anaesthetized spontaneously breathing pigs. Intravenous bolus administration of synthetic ET-1 (40–100 pmol/kg) caused a transient decrease followed by a long-lasting increase in mean pulmonary arterial pressure and dose dependent vasoconstriction both in the systemic and pulmonary circulations. The effect on pulmonary arterial pressure was biphasic, with an initial transient fall followed by a long-lasting dose dependent increase. A biphasic response of the systemic mean arterial pressure was demonstrated only at a high dose of ET-1 (100 pmol/kg). ET-1 administration did not significantly change breathing pattern or phasic vagal input, but caused a significant decrease in passive compliance. Passive resistances or active compliance and resistances of the respiratory system were not modified. These results suggest that in the pig ET-1 is a more potent constrictor of vascular than of bronchial smooth muscle. The vasoconstrictor activity was greater in the pulmonary than the systemic circulations
Thermodynamics of the 3-State Potts Spin Chain
We demonstrate the relation of the infrared anomaly of conformal field theory
with entropy considerations of finite temperature thermodynamics for the
3-state Potts chain. We compute the free energy and compute the low temperature
specific heat for both the ferromagnetic and anti-ferromagnetic spin chains,
and find the central charges for both.Comment: 18 pages, LaTex. Preprint # ITP-SB-92-60. References added and first
section expande
Spin operator matrix elements in the superintegrable chiral Potts quantum chain
We derive spin operator matrix elements between general eigenstates of the
superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our
starting point is the extended Onsager algebra recently proposed by R.Baxter.
For each pair of spaces (Onsager sectors) of the irreducible representations of
the Onsager algebra, we calculate the spin matrix elements between the
eigenstates of the Hamiltonian of the quantum chain in factorized form, up to
an overall scalar factor. This factor is known for the ground state Onsager
sectors. For the matrix elements between the ground states of these sectors we
perform the thermodynamic limit and obtain the formula for the order
parameters. For the Ising quantum chain in a transverse field (N=2 case) the
factorized form for the matrix elements coincides with the corresponding
expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur
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