23,546 research outputs found
The topological classification of one-dimensional symmetric quantum walks
We give a topological classification of quantum walks on an infinite 1D
lattice, which obey one of the discrete symmetry groups of the tenfold way,
have a gap around some eigenvalues at symmetry protected points, and satisfy a
mild locality condition. No translation invariance is assumed. The
classification is parameterized by three indices, taking values in a group,
which is either trivial, the group of integers, or the group of integers modulo
2, depending on the type of symmetry. The classification is complete in the
sense that two walks have the same indices if and only if they can be connected
by a norm continuous path along which all the mentioned properties remain
valid. Of the three indices, two are related to the asymptotic behaviour far to
the right and far to the left, respectively. These are also stable under
compact perturbations. The third index is sensitive to those compact
perturbations which cannot be contracted to a trivial one. The results apply to
the Hamiltonian case as well. In this case all compact perturbations can be
contracted, so the third index is not defined. Our classification extends the
one known in the translation invariant case, where the asymptotic right and
left indices add up to zero, and the third one vanishes, leaving effectively
only one independent index. When two translationally invariant bulks with
distinct indices are joined, the left and right asymptotic indices of the
joined walk are thereby fixed, and there must be eigenvalues at or
(bulk-boundary correspondence). Their location is governed by the third index.
We also discuss how the theory applies to finite lattices, with suitable
homogeneity assumptions.Comment: 36 pages, 7 figure
Very small grains in the Milky Way and external galaxies
These studies of the infrared colors of reflection nebulae, HL HI clouds, HII regions and external galaxies have shown the following results. Different classes of objects locate in different regions on the R vs F sub v (60)/F sub v (100) diagram. This is determined both by differences in dust properties and by differences in the illuminating radiation field. For example, HL clouds and reflection nebulae almost have the same behavior since both are in the diffuse Interstellar Medium (ISM) and can be expected to have similar grain populations; the small difference in their infrared colors can be explained by the difference of the illuminating radiation field. On the other hand, the dramatic difference of R=vF sub v (12)/F sub v (far IR) between HII region and diffuse ISM may be due to the destruction of the Very Small Grain (VSG) component in the HII regions, although radiation transfer effects may play a part as well. The ratio R=vF sub v (12)/F sub v (far IR) is approximately constant in normal spiral galaxies. This implies that the mass ratio b=Mass (VSG)/Mass (dust) does not vary greatly from one galaxy to another
Hadron-Hadron Interactions from Lattice QCD: isospin-1 scattering length
We present results for the interaction of two kaons at maximal isospin. The
calculation is based on flavour gauge configurations generated by
the European Twisted Mass Collaboration with pion masses ranging from about
to at three values of the lattice spacing. The
elastic scattering length is calculated at several values of the
bare strange and light quark masses. We find as
the result of a combined extrapolation to the continuum and to the physical
point, where the first error is statistical, and the three following are
systematical. This translates to .Comment: 28 pages, 18 tables, 14 figure
Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv: 1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrodinger equation. We show exponential behaviour, and give a practical method for computing the decay constants
Hadron-Hadron Interactions from Lattice QCD: isospin-2 scattering length
We present results for the scattering length using
twisted mass lattice QCD for three values of the lattice spacing and a range of
pion mass values. Due to the use of Laplacian Heaviside smearing our
statistical errors are reduced compared to previous lattice studies. A detailed
investigation of systematic effects such as discretisation effects, volume
effects, and pollution of excited and thermal states is performed. After
extrapolation to the physical point using chiral perturbation theory at NLO we
obtain .Comment: Edited for typos, overhauled figures, more detailed comparison to
existing lattice result
Simulation of seismic events induced by CO2 injection at In Salah, Algeria
Date of Acceptance: 18/06/2015 Acknowledgments The authors would like to thank the operators of the In Salah JV and JIP, BP, Statoil and Sonatrach, for providing the data shown in this paper, and for giving permission to publish. Midland Valley Exploration are thanked for the use of their Move software for geomechanical restoration. JPV is a Natural Environment Research Council (NERC) Early Career Research Fellow (Grant NE/I021497/1) and ALS is funded by a NERC Partnership Research Grant (Grant NE/I010904).Peer reviewedPublisher PD
Norm Optimal Iterative Learning Control with Application to Problems in Accelerator based Free Electron Lasers and Rehabilitation Robotics
This paper gives an overview of the theoretical basis of the norm optimal approach to iterative learning control followed by results that describe more recent work which has experimentally benchmarking the performance that can be achieved. The remainder of then paper then describes its actual application to a physical process and a very novel application in stroke rehabilitation
- …