100 research outputs found
Exact solutions for a universal set of quantum gates on a family of iso-spectral spin chains
We find exact solutions for a universal set of quantum gates on a scalable
candidate for quantum computers, namely an array of two level systems. The
gates are constructed by a combination of dynamical and geometrical
(non-Abelian) phases. Previously these gates have been constructed mostly on
non-scalable systems and by numerical searches among the loops in the manifold
of control parameters of the Hamiltonian.Comment: 1 figure, Latex, 8 pages, Accepted for publication in Physical Review
The matrix product representations for all valence bond states
We introduce a simple representation for irreducible spherical tensor
operators of the rotation group of arbitrary integer or half integer rank and
use these tensor operators to construct matrix product states corresponding to
all the variety of valence-bond states proposed in the
Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully
dimerized states of arbitrary spins, with uniform or alternating patterns of
spins, which are ground states of Hamiltonians with nearest and next-nearest
neighbor interactions, and the partially dimerized or AKLT/VBS (Valence Bond
Solid) states, which are constructed from them by projection. The latter states
are translation-invariant ground states of Hamiltonians with nearest-neighbor
interactions.Comment: 24 pages, references added, the version which appears in the journa
General Reaction-Diffusion Processes With Separable Equations for Correlation Functions
We consider general multi-species models of reaction diffusion processes and
obtain a set of constraints on the rates which give rise to closed systems of
equations for correlation functions. Our results are valid in any dimension and
on any type of lattice. We also show that under these conditions the evolution
equations for two point functions at different times are also closed. As an
example we introduce a class of two species models which may be useful for the
description of voting processes or the spreading of epidemics.Comment: 17 pages, Latex, No figure
Bicovariant Differential Geometry of the Quantum Group
There are only two quantum group structures on the space of two by two
unimodular matrices, these are the and the [9-13] quantum
groups. One can not construct a differential geometry on , which at
the same time is bicovariant, has three generators, and satisfies the Liebnitz
rule. We show that such a differential geometry exists for the quantum group
and derive all of its properties
h-deformation of Gr(2)
The -deformation of functions on the Grassmann matrix group is
presented via a contraction of . As an interesting point, we have seen
that, in the case of the -deformation, both R-matrices of and
are the same
Exact symmetry breaking ground states for quantum spin chains
We introduce a family of spin-1/2 quantum chains, and show that their exact
ground states break the rotational and translational symmetries of the original
Hamiltonian. We also show how one can use projection to construct a spin-3/2
quantum chain with nearest neighbor interaction, whose exact ground states
break the rotational symmetry of the Hamiltonian. Correlation functions of both
models are determined in closed form. Although we confine ourselves to
examples, the method can easily be adapted to encompass more general models.Comment: 4 pages, RevTex. 4 figures, minor changes, new reference
Multispecies reaction-diffusion systems
Multispecies reaction-diffusion systems, for which the time evolution
equation of correlation functions become a closed set, are considered. A formal
solution for the average densities is found. Some special interactions and the
exact time dependence of the average densities in these cases are also studied.
For the general case, the large time behaviour of the average densities has
also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.
Maps between Deformed and Ordinary Gauge Fields
In this paper, we introduce a map between the q-deformed gauge fields defined
on the GL-covariant quantum hyperplane and the ordinary gauge fields.
Perturbative analysis of the q-deformed QED at the classical level is presented
and gauge fixing la BRST is discussed. An other star product
defined on the hybrid % -plane is explicitly constructed .Comment: 10 page
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
Duality for the Jordanian Matrix Quantum Group
We find the Hopf algebra dual to the Jordanian matrix quantum group
. As an algebra it depends only on the sum of the two parameters
and is split in two subalgebras: (with three generators) and
(with one generator). The subalgebra is a central Hopf subalgebra of
. The subalgebra is not a Hopf subalgebra and its coalgebra
structure depends on both parameters. We discuss also two one-parameter special
cases: and . The subalgebra is a Hopf algebra and
coincides with the algebra introduced by Ohn as the dual of . The
subalgebra is isomorphic to as an algebra but has a
nontrivial coalgebra structure and again is not a Hopf subalgebra of
.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC
nonlinear ma
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