1,023 research outputs found
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
Partitions with Prescribed Hook Differences
We investigate partition identities related to off-diagonal hook differences. Our results generalize previous extensions of the Rogers—Ramanujan identities. The identity of the related polynomials with constructs in statistical mechanics is discussed
Order Parameters of the Dilute A Models
The free energy and local height probabilities of the dilute A models with
broken \Integer_2 symmetry are calculated analytically using inversion and
corner transfer matrix methods. These models possess four critical branches.
The first two branches provide new realisations of the unitary minimal series
and the other two branches give a direct product of this series with an Ising
model. We identify the integrable perturbations which move the dilute A models
away from the critical limit. Generalised order parameters are defined and
their critical exponents extracted. The associated conformal weights are found
to occur on the diagonal of the relevant Kac table. In an appropriate regime
the dilute A model lies in the universality class of the Ising model in a
magnetic field. In this case we obtain the magnetic exponent
directly, without the use of scaling relations.Comment: 53 pages, LaTex, ITFA 93-1
On two 10th order mock theta identities
We give short proofs of conjectural identities due to Gordon and McIntosh
involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa
Competing density-wave orders in a one-dimensional hard-boson model
We describe the zero-temperature phase diagram of a model of bosons,
occupying sites of a linear chain, which obey a hard-exclusion constraint: any
two nearest-neighbor sites may have at most one boson. A special case of our
model was recently proposed as a description of a ``tilted'' Mott insulator of
atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to
generate the transfer matrix of Baxter's hard-square model. Aided by exact
solutions of a number of special cases, and by numerical studies, we obtain a
phase diagram containing states with long-range density-wave order with period
2 and period 3, and also a floating incommensurate phase. Critical theories for
the various quantum phase transitions are presented. As a byproduct, we show
how to compute the Luttinger parameter in integrable theories with
hard-exclusion constraints.Comment: 16 page
Spectral Decomposition of Path Space in Solvable Lattice Model
We give the {\it spectral decomposition} of the path space of the
U_q(\hatsl) vertex model with respect to the local energy functions. The
result suggests the hidden Yangian module structure on the \hatsl level
integrable modules, which is consistent with the earlier work [1] in the level
one case. Also we prove the fermionic character formula of the \hatsl level
integrable representations in consequence.Comment: 27 pages, Plain Tex, epsf.tex, 7 figures; minor revision. identical
with the version to be published in Commun.Math.Phy
Stable lyophilised gel vehicles for vaginal administration of recombinant C-clade HIV-1 trimeric CN54gp140
Adiabatic Output Coupling of a Bose Gas at Finite Temperatures
We develop a general theory of adiabatic output coupling from trapped atomic
Bose-Einstein Condensates at finite temperatures. For weak coupling, the output
rate from the condensate, and the excited levels in the trap, settles in a time
proportional to the inverse of the spectral width of the coupling to the output
modes. We discuss the properties of the output atoms in the quasi-steady-state
where the population in the trap is not appreciably depleted. We show how the
composition of the output beam, containing condensate and thermal component,
may be controlled by changing the frequency of the output coupler. This
composition determines the first and second order coherence of the output beam.
We discuss the changes in the composition of the bose gas left in the trap and
show how nonresonant output coupling can stimulate either the evaporation of
thermal excitations in the trap or the growth of non-thermal excitations, when
pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from
the previous submission have been fixe
On manifolds with nonhomogeneous factors
We present simple examples of finite-dimensional connected homogeneous spaces
(they are actually topological manifolds) with nonhomogeneous and nonrigid
factors. In particular, we give an elementary solution of an old problem in
general topology concerning homogeneous spaces
Dilogarithm Identities in Conformal Field Theory and Group Homology
Recently, Rogers' dilogarithm identities have attracted much attention in the
setting of conformal field theory as well as lattice model calculations. One of
the connecting threads is an identity of Richmond-Szekeres that appeared in the
computation of central charges in conformal field theory. We show that the
Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be
interpreted as a lift of a generator of the third integral homology of a finite
cyclic subgroup sitting inside the projective special linear group of all real matrices viewed as a {\it discrete} group. This connection
allows us to clarify a few of the assertions and conjectures stated in the work
of Nahm-Recknagel-Terhoven concerning the role of algebraic -theory and
Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related
to hyperbolic 3-manifolds as suggested but is more appropriately related to the
group manifold of the universal covering group of the projective special linear
group of all real matrices viewed as a topological group. This
also resolves the weaker version of the conjecture as formulated by Kirillov.
We end with the summary of a number of open conjectures on the mathematical
side.Comment: 20 pages, 2 figures not include
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