3,483 research outputs found
The stationary measure for diagonal quantum walk with one defect
This study is motivated by the previous work [14]. We treat 3 types of the
one-dimensional quantum walks (QWs), whose time evolutions are described by
diagonal unitary matrix, and diagonal unitary matrices with one defect. In this
paper, we call the QW defined by diagonal unitary matrices, "the diagonal QW",
and we consider the stationary distributions of generally 2-state diagonal QW
with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW
with one defect. One of the purposes of our study is to characterize the QWs by
the stationary measure, which may lead to answer the basic and natural
question, "What the stationary measure is for one-dimensional QWs ?". In order
to analyze the stationary distribution, we focus on the corresponding
eigenvalue problems and the definition of the stationary measure.Comment: 10 page
Stationary measure for two-state space-inhomogeneous quantum walk in one dimension
We consider the two-state space-inhomogeneous coined quantum walk (QW) in one
dimension. For a general setting, we obtain the stationary measure of the QW by
solving the eigenvalue problem. As a corollary, stationary measures of the
multi-defect model and space-homogeneous QW are derived. The former is a
generalization of the previous works on one-defect model and the latter is a
generalization of the result given by Konno and Takei (2015).Comment: 15 pages, revised version, Yokohama Mathematical Journal (in press
Braiding Interactions in Anyonic Quantum Walks
The anyonic quantum walk is a dynamical model describing a single anyon
propagating along a chain of stationary anyons and interacting via mutual
braiding statistics. We review the recent results on the effects of braiding
statistics in anyonic quantum walks in quasi-one dimensional ladder geometries.
For anyons which correspond to spin-1/2 irreps of the quantum groups ,
the non-Abelian species gives rise to entanglement between the
walker and topological degrees of freedom which is quantified by quantum link
invariants over the trajectories of the walk. The decoherence is strong enough
to reduce the walk on the infinite ladder to classical like behaviour. We also
present numerical results on mixing times of or Ising model anyon
walks on cyclic graphs. Finally, the possible experimental simulation of the
anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International
Conference on Theoretical Physics (ICTP 2012
Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems
We demonstrate fractal noise in the quantum evolution of wave packets moving
either ballistically or diffusively in periodic and quasiperiodic tight-binding
lattices, respectively. For the ballistic case with various initial
superpositions we obtain a space-time self-affine fractal which
verify the predictions by Berry for "a particle in a box", in addition to
quantum revivals. For the diffusive case self-similar fractal evolution is also
obtained. These universal fractal features of quantum theory might be useful in
the field of quantum information, for creating efficient quantum algorithms,
and can possibly be detectable in scattering from nanostructures.Comment: 9 pages, 8 postscript figure
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