4,090 research outputs found
Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2)
introduced earlier by one of the authors. Our construction is based on a new
set of generating series in the quantum affine algebra U_q(^sl_2), which are
elliptic analogs of the Drinfeld currents. They enable us to identify
U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra
generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L
operator satisfying the dynamical RLL relation in the presence of the central
element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners'
of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated
on in the text. We also present vertex operators with higher level/spin in the
free field representation.Comment: 49 pages, (AMS-)LaTeX ; added an explanation of integration contours;
added comments. To appear in Comm. Math. Phys. Numbering of equations is
correcte
Free Field Approach to the Dilute A_L Models
We construct a free field realization of vertex operators of the dilute A_L
models along with the Felder complex. For L=3, we also study an E_8 structure
in terms of the deformed Virasoro currents.Comment: (AMS-)LaTeX(2e), 43page
Weak limits for quantum random walks
We formulate and prove a general weak limit theorem for quantum random walks
in one and more dimensions. With denoting position at time , we show
that converges weakly as to a certain distribution which
is absolutely continuous and of bounded support. The proof is rigorous and
makes use of Fourier transform methods. This approach simplifies and extends
certain preceding derivations valid in one dimension that make use of
combinatorial and path integral methods
Localization of the Grover walks on spidernets and free Meixner laws
A spidernet is a graph obtained by adding large cycles to an almost regular
tree and considered as an example having intermediate properties of lattices
and trees in the study of discrete-time quantum walks on graphs. We introduce
the Grover walk on a spidernet and its one-dimensional reduction. We derive an
integral representation of the -step transition amplitude in terms of the
free Meixner law which appears as the spectral distribution. As an application
we determine the class of spidernets which exhibit localization. Our method is
based on quantum probabilistic spectral analysis of graphs.Comment: 32 page
Absorption problems for quantum walks in one dimension
This paper treats absorption problems for the one-dimensional quantum walk
determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N
is finite or infinite by using a new path integral approach based on an
orthonormal basis P, Q, R and S of the vector space of complex 2 times 2
matrices. Our method studied here is a natural extension of the approach in the
classical random walk.Comment: 15 pages, small corrections, journal reference adde
Continuous-time quantum walk on integer lattices and homogeneous trees
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and
infinite homogeneous trees. By using the generating function method, we compute
the limit of the average probability distribution for the general isotropic
walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous
trees. In addition, we compute the asymptotic approximation for the probability
of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page
Entanglement measurement with discrete multiple coin quantum walks
Within a special multi-coin quantum walk scheme we analyze the effect of the
entanglement of the initial coin state. For states with a special entanglement
structure it is shown that this entanglement can be meausured with the mean
value of the walk, which depends on the i-concurrence of the initial coin
state. Further on the entanglement evolution is investigated and it is shown
that the symmetry of the probability distribution is reflected by the symmetry
of the entanglement distribution.Comment: 9 pages, IOP styl
- …