817 research outputs found
Conductance of tubular nanowires with disorder
We calculate the conductance of tubular-shaped nanowires having many
potential scatterers at random positions. Our approach is based on the
scattering matrix formalism and our results analyzed within the scaling theory
of disordered conductors. When increasing the energy the conductance for a big
enough number of impurities in the tube manifests a systematic evolution from
the localized to the metallic regimes. Nevertheless, a conspicuous drop in
conductance is predicted whenever a new transverse channel is open. Comparison
with the semiclassical calculation leading to purely ohmic behavior is made.Comment: 8 pages, 5 figure
Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder
We review recent work on the random hopping problem in a
quasi-one-dimensional geometry of N coupled chains (quantum wire with
off-diagonal disorder). Both density of states and conductance show a
remarkable dependence on the parity of N. The theory is compared to numerical
simulations.Comment: 8 pages, to appear in Physica E (special issue on Dynamics of Complex
Systems); 6 figure
Effective Hamiltonian Theory and Its Applications in Quantum Information
This paper presents a useful compact formula for deriving an effective
Hamiltonian describing the time-averaged dynamics of detuned quantum systems.
The formalism also works for ensemble-averaged dynamics of stochastic systems.
To illustrate the technique we give examples involving Raman processes,
Bloch-Siegert shifts and Quantum Logic Gates.Comment: 5 pages, 3 figures, to be published in Canadian Journal of Physic
Fokker-Planck equations and density of states in disordered quantum wires
We propose a general scheme to construct scaling equations for the density of
states in disordered quantum wires for all ten pure Cartan symmetry classes.
The anomalous behavior of the density of states near the Fermi level for the
three chiral and four Bogoliubov-de Gennes universality classes is analysed in
detail by means of a mapping to a scaling equation for the reflection from a
quantum wire in the presence of an imaginary potential.Comment: 10 pages, 5 figures, revised versio
Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion
We present a fully analytic calculation of the Higgs boson transverse
momentum and rapidity distributions, for nonzero Higgs , at
next-to-leading order in the infinite-top-mass approximation. We separate the
cross section into a part that contains the dominant soft, virtual, collinear,
and small--enhanced contributions, and the remainder, which is
organized by the contributions due to different parton helicities. We use this
cross section to investigate analytically the small- limit and compare
with the expectation from the resummation of large logarithms of the type
. We also compute numerically the cross section at moderate
where a fixed-order calculation is reliable. We find a -factor
that varies from , and a reduction in the scale dependence, as
compared to leading order. Our analysis suggests that the contribution of
current parton distributions to the total uncertainty on this cross section at
the LHC is probably less than that due to uncalculated higher orders.Comment: 40 pages, 10 figures, JHEP style (minor changes, added reference
The random phase property and the Lyapunov Spectrum for disordered multi-channel systems
A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum
Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important
model system for the high- superconductors based on cuprates. Using the
technique of self-similar continuous unitary transformations we derive
effective Hamiltonians for the charge motion in these ladders. The key
advantage of this technique is that it provides effective models explicitly in
the thermodynamic limit. A real space restriction of the generator of the
transformation allows us to explore the experimentally relevant parameter
space. From the effective Hamiltonians we calculate the dispersions for single
holes. Further calculations will enable the calculation of the interaction of
two holes so that a handle of Cooper pair formation is within reach.Comment: 16 pages, 26 figure
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
Surface effects in multiband superconductors. Application to MgB
Metals with many bands at the Fermi level can have different band dependent
gaps in the superconducting state. The absence of translational symmetry at an
interface can induce interband scattering and modify the superconducting
properties. We dicuss the relevance of these effects to recent experiments in
MgB
Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum
The diffraction spectrum of coherent waves scattered from fractal supports is
calculated exactly. The fractals considered are of the class generated
iteratively by successive dilations and translations, and include
generalizations of the Cantor set and Sierpinski carpet as special cases. Also
randomized versions of these fractals are treated. The general result is that
the diffraction intensities obey a strict recursion relation, and become
self-affine in the limit of large iteration number, with a self-affinity
exponent related directly to the fractal dimension of the scattering object.
Applications include neutron scattering, x-rays, optical diffraction, magnetic
resonance imaging, electron diffraction, and He scattering, which all display
the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at
http://www.fh.huji.ac.il/~dani
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