10,226 research outputs found
Globe-hopping
We consider versions of the grasshopper problem (Goulko & Kent 2017 Proc. R. Soc. A473, 20170494) on the circle and the sphere, which are relevant to Bell inequalities. For a circle of circumference 2π, we show that for unconstrained lawns of any length and arbitrary jump lengths, the supremum of the probability for the grasshopper’s jump to stay on the lawn is one. For antipodal lawns, which by definition contain precisely one of each pair of opposite points and have length π, we show this is true except when the jump length ϕ is of the form π(p/q) with p, q coprime and p odd. For these jump lengths, we show the optimal probability is 1 − 1/q and construct optimal lawns. For a pair of antipodal lawns, we show that the optimal probability of jumping from one onto the other is 1 − 1/q for p, q coprime, p odd and q even, and one in all other cases. For an antipodal lawn on the sphere, it is known (Kent & Pitalúa-García 2014 Phys. Rev. A90, 062124) that if ϕ = π/q, where q∈N, then the optimal retention probability of 1 − 1/q for the grasshopper’s jump is provided by a hemispherical lawn. We show that in all other cases where 0 < ϕ < π/2, hemispherical lawns are not optimal, disproving the hemispherical colouring maximality hypotheses (Kent & Pitalúa-García 2014 Phys. Rev. A90, 062124). We discuss the implications for Bell experiments and related cryptographic tests
In situ method for power re-equalization of wavelength pulses inside of OCDMA codes
A simple in-situ method to equalize power among individual wavelengths pulses representing two-dimensional wavelength-hopping time-spreading OCDMA code originally generated by a fibre Bragg grating-based OCDMA encoder is presented. Experimental data obtained in a field-based multiuser OCDMA testbed shows that applying this method results in system performance enhancements which was demonstrated by observing improved bit error rate (BER) during the field trials
Evidence of robust 2D transport and Efros-Shklovskii variable range hopping in disordered topological insulator (Bi2Se3) nanowires
We report the experimental observation of variable range hopping conduction
in focused-ion-beam (FIB) fabricated ultra-narrow nanowires of topological
insulator (Bi2Se3). The value of the exponent in the hopping equation was
extracted as ~ 1/2 for different widths of nanowires, which is the proof of the
presence of Efros-Shklovskii hopping transport mechanism in a strongly
disordered system. High localization lengths (0.5nm, 20nm) were calculated for
the devices. A careful analysis of the temperature dependent fluctuations
present in the magnetoresistance curves, using the standard Universal
Conductance Fluctuation theory, indicates the presence of 2D topological
surface states. Also, the surface state contribution to the conductance was
found very close to one conductance quantum. We believe that our experimental
findings shed light on the understanding of quantum transport in disordered
topological insulator based nanostructures.Comment: 14pages, 4 figure
Dielectric properties of Li2O-3B2O3 glasses
The frequency and temperature dependence of the dielectric constant and the
electrical conductivity of the transparent glasses in the composition
Li2O-3B2O3 (LBO) were investigated in the 100 Hz- 10 MHz frequency range. The
dielectric constant and the loss in the low frequency regime were electrode
material dependent. Dielectric and electrical relaxations were respectively
analyzed using the Cole-Cole and electric modulus formalisms. The dielectric
relaxation mechanism was discussed in the framework of electrode and charge
carrier (hopping of the ions) related polarization using generalized Cole-Cole
expression. The frequency dependent electrical conductivity was rationalized
using Jonscher's power law. The activation energy associated with the dc
conductivity was 0.80 \pm 0.02 eV, which was ascribed to the motion of Li+ ions
in the glass matrix. The activation energy associated with dielectric
relaxation was almost equal to that of the dc conductivity, indicating that the
same species took part in both the processes. Temperature dependent behavior of
the frequency exponent (n) suggested that the correlated barrier hopping model
was the most apposite to rationalize the electrical transport phenomenon in
Li2O-3B2O3 glasses. These glasses on heating at 933 K/10h resulted in the known
non-linear optical phase LiB3O5.Comment: 32 pages, 13 figure
Graphene via large N I: Renormalization
We analyze the competing effects of moderate to strong Coulomb
electron-electron interactions and weak quenched disorder in graphene. Using a
one-loop renormalization group calculation controlled within the large-N
approximation, we demonstrate that, at successively lower energy (temperature
or chemical potential) scales, a type of non-Abelian vector potential disorder
always asserts itself as the dominant elastic scattering mechanism for generic
short-ranged microscopic defect distributions. Vector potential disorder is
tied to both elastic lattice deformations ("ripples") and topological lattice
defects. We identify several well-defined scaling regimes, for which we provide
scaling predictions for the electrical conductivity and thermopower, valid when
the inelastic lifetime due to interactions exceeds the elastic lifetime due to
disorder. Coulomb interaction effects should figure strongly into the physics
of suspended graphene films, where rs > 1; we expect vector potential disorder
to play an important role in the description of transport in such films.Comment: 25 pages, 21 figure
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