42,211 research outputs found
Zeta-like Multizeta Values for higher genus curves
We prove or conjecture several relations between the multizeta values for
positive genus function fields of class number one, focusing on the zeta-like
values, namely those whose ratio with the zeta value of the same weight is
rational (or conjecturally equivalently algebraic). These are the first known
relations between multizetas, which are not with prime field coefficients. We
seem to have one universal family. We also find that interestingly the
mechanism with which the relations work is quite different from the rational
function field case, raising interesting questions about the expected motivic
interpretation in higher genus. We provide some data in support of the guesses.Comment: Expository revisions plus appendices containing proofs of more cases
of conjecture
Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene
We investigate the transmission properties of quasiperiodic or aperiodic
structures based on graphene arranged according to the Cantor sequence. In
particular, we have found self-similar behaviour in the transmission spectra,
and most importantly, we have calculated the scalability of the spectra. To do
this, we implement and propose scaling rules for each one of the fundamental
parameters: generation number, height of the barriers and length of the system.
With this in mind we have been able to reproduce the reference transmission
spectrum, applying the appropriate scaling rule, by means of the scaled
transmission spectrum. These scaling rules are valid for both normal and
oblique incidence, and as far as we can see the basic ingredients to obtain
self-similar characteristics are: relativistic Dirac electrons, a self-similar
structure and the non-conservation of the pseudo-spin. This constitutes a
reduction of the number of conditions needed to observe self-similarity in
graphene-based structures, see D\'iaz-Guerrero et al. [D. S. D\'iaz-Guerrero,
L. M. Gaggero-Sager, I. Rodr\'iguez-Vargas, and G. G. Naumis,
arXiv:1503.03412v1, 2015]
Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder
With Monte Carlo methods, we investigate the universality class of the
depinning transition in the two-dimensional Ising model with quenched random
fields. Based on the short-time dynamic approach, we accurately determine the
depinning transition field and both static and dynamic critical exponents. The
critical exponents vary significantly with the form and strength of the random
fields, but exhibit independence on the updating schemes of the Monte Carlo
algorithm. From the roughness exponents and , one
may judge that the depinning transition of the random-field Ising model belongs
to the new dynamic universality class with
and . The crossover from the second-order phase transition
to the first-order one is observed for the uniform distribution of the random
fields, but it is not present for the Gaussian distribution.Comment: 16 pages, 16 figures, 3 table
Generation of twin Fock states via transition from a two-component Mott insulator to a superfluid
We propose the dynamical creation of twin Fock states, which exhibit
Heisenberg limited interferometric phase sensitivities, in an optical lattice.
In our scheme a two-component Mott insulator with two bosonic atoms per lattice
site is melted into a superfluid. This process transforms local correlations
between hyperfine states of atom pairs into multi-particle correlations
extending over the whole system. The melting time does not scale with the
system size which makes our scheme experimentally feasible.Comment: 4 pages, 4 figure
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