153 research outputs found
Representations of the quantum matrix algebra
It is shown that the finite dimensional irreducible representaions of the
quantum matrix algebra ( the coordinate ring of ) exist only when both q and p are roots of unity. In this case th e space of
states has either the topology of a torus or a cylinder which may be thought of
as generalizations of cyclic representations.Comment: 20 page
Q-Boson Representation of the Quantum Matrix Algebra
{Although q-oscillators have been used extensively for realization of quantum
universal enveloping algebras,such realization do not exist for quantum matrix
algebras ( deformation of the algebra of functions on the group ). In this
paper we first construct an infinite dimensional representation of the quantum
matrix algebra (the coordinate ring of and then use
this representation to realize by q-bosons.}Comment: pages 18 ,report # 93-00
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
An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update
Within the formalism of matrix product ansatz, we study a two-species
asymmetric exclusion process with backward and forward site-ordered sequential
update. This model, which was originally introduced with the random sequential
update, describes a two-way traffic flow with a dynamic impurity and shows a
phase transition between the free flow and traffic jam. We investigate the
characteristics of this jamming and examine similarities and differences
between our results and those with random sequential update.Comment: 25 pages, Revtex, 7 ps file
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter ,
interpolating between the completely asymmetric processes [1] (for ) and the n=1 drop-push models [2] (for ). For arbitrary \la,
the model describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the exact solution of the
master equation .Comment: 14 pages, LaTe
Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
An ASEP with two species of particles and different hopping rates is
considered on a ring. Its integrability is proved and the Nested Algebraic
Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary
numbers of particles of each type, generalizing the results of Derrida and
Evans. We present also formulas for the total velocity of particles of a given
type and their limit for large size of the system and finite densities of the
particles.Comment: 14 page
On the Phase Covariant Quantum Cloning
It is known that in phase covariant quantum cloning the equatorial states on
the Bloch sphere can be cloned with a fidelity higher than the optimal bound
established for universal quantum cloning. We generalize this concept to
include other states on the Bloch sphere with a definite component of spin.
It is shown that once we know the component, we can always clone a state
with a fidelity higher than the universal value and that of equatorial states.
We also make a detailed study of the entanglement properties of the output
copies and show that the equatorial states are the only states which give rise
to separable density matrix for the outputs.Comment: Revtex4, 6 pages, 5 eps figure
A multi-species asymmetric exclusion process;steady state and correlation functions on a periodic lattice
By generalizing the algebra of operators of the Asymmetric Simple Exclusion
Process (ASEP), a multi-species ASEP in which particles can overtake each
other,is defined on both open and closed one dimensional chains. On the ring
the steady state and the correlation functions are obtained exactly. The
relation to particle hopping models of traffic and the possibility of shock
waves in open systems is discussed. The effect of the boundary condition on the
steady state properties of the bulk is studied.Comment: References added, typos correcte
A systematic construction of completely integrable Hamiltonians from coalgebras
A universal algorithm to construct N-particle (classical and quantum)
completely integrable Hamiltonian systems from representations of coalgebras
with Casimir element is presented. In particular, this construction shows that
quantum deformations can be interpreted as generating structures for integrable
deformations of Hamiltonian systems with coalgebra symmetry. In order to
illustrate this general method, the algebra and the oscillator
algebra are used to derive new classical integrable systems including a
generalization of Gaudin-Calogero systems and oscillator chains. Quantum
deformations are then used to obtain some explicit integrable deformations of
the previous long-range interacting systems and a (non-coboundary) deformation
of the Poincar\'e algebra is shown to provide a new
Ruijsenaars-Schneider-like Hamiltonian.Comment: 26 pages, LaTe
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
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