29,831 research outputs found
The spectrum of a vertex model and related spin one chain sitting in a genus five curve
We derive the transfer matrix eigenvalues of a three-state vertex model whose
weights are based on a -matrix not of difference form with spectral
parameters lying on a genus five curve. We have shown that the basic building
blocks for both the transfer matrix eigenvalues and Bethe equations can be
expressed in terms of meromorphic functions on an elliptic curve. We discuss
the properties of an underlying spin one chain originated from a particular
choice of the -matrix second spectral parameter. We present
numerical and analytical evidences that the respective low-energy excitations
can be gapped or massless depending on the strength of the interaction
coupling. In the massive phase we provide analytical and numerical evidences in
favor of an exact expression for the lowest energy gap. We point out that the
critical point separating these two distinct physical regimes coincides with
the one in which the weights geometry degenerate into union of genus one
curves.Comment: 22 pages, 12 figure
Integrable Vertex Models with General Twists
We review recent progress towards the solution of exactly solved isotropic
vertex models with arbitrary toroidal boundary conditions. Quantum space
transformations make it possible the diagonalization of the corresponding
transfer matrices by means of the quantum inverse scattering method. Explicit
expressions for the eigenvalues and Bethe ansatz equations of the twisted
isotropic spin chains based on the , and Lie algebras are
presented. The applicability of this approach to the eight vertex model with
non-diagonal twists is also discussed.Comment: 9 pages, Proceedings of Recent Progress in Solvable Models: RIMS
Project, Kyoto, Japan, 20-23 July 200
Algebraic Geometry methods associated to the one-dimensional Hubbard model
In this paper we study the covering vertex model of the one-dimensional
Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry.
We show that the Lax operator sits in a genus one curve which is not isomorphic
but only isogenous to the curve suitable for the AdS/CFT context. We provide an
uniformization of the Lax operator in terms of ratios of theta functions
allowing us to establish relativistic like properties such as crossing and
unitarity. We show that the respective -matrix weights lie on an
Abelian surface being birational to the product of two elliptic curves with
distinct -invariants. One of the curves is isomorphic to that of
the Lax operator but the other is solely fourfold isogenous. These results
clarify the reason the -matrix can not be written using only
difference of spectral parameters of the Lax operator.Comment: 24 page
Renormalized transport of inertial particles in surface flows
Surface transport of inertial particles is investigated by means of the
perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)),
which is valid in the case the deflections induced on the particle trajectories
by the fluid flow can be considered small. We consider a class of compressible
random velocity fields, in which the effect of recirculations is modelled by an
oscillatory component in the Eulerian time correlation profile. The main issue
we address here is whether fluid velocity fluctuations, in particular the
effect of recirculation, may produce nontrivial corrections to the streaming
particle velocity. Our result is that a small (large) degree of recirculation
is associated with a decrease (increase) of streaming with respect to a
quiescent fluid. The presence of this effect is confirmed numerically, away
from the perturbative limit. Our approach also allows us to calculate the
explicit expression for the eddy diffusivity, and to compare the efficiency of
diffusive and ballistic transport.Comment: 18 pages, 13 figures, submitted to JF
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