14,985 research outputs found
Factorization of the Non-Stationary Schrodinger Operator
We consider a factorization of the non-stationary Schrodinger operator based
on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based
on the fundamental solution for the parabolic Dirac operators, we shall
construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we
will describe how to solve the nonlinear Schrodinger equation using Banach
fixed point theorem.Comment: Accepted for publication in Advances in Applied Clifford Algebra
A theorem regarding families of topologically non-trivial fermionic systems
We introduce a Hamiltonian for fermions on a lattice and prove a theorem
regarding its topological properties. We identify the topological criterion as
a topological invariant (the Pfaffian
polynomial). The topological invariant is not only the first Chern number, but
also the sign of the Pfaffian polynomial coming from a notion of duality. Such
Hamiltonian can describe non-trivial Chern insulators, single band
superconductors or multiorbital superconductors. The topological features of
these families are completely determined as a consequence of our theorem. Some
specific model examples are explicitly worked out, with the computation of
different possible topological invariants.Comment: 6 page
Volume change of bulk metals and metal clusters due to spin-polarization
The stabilized jellium model (SJM) provides us a method to calculate the
volume changes of different simple metals as a function of the spin
polarization, , of the delocalized valence electrons. Our calculations
show that for bulk metals, the equilibrium Wigner-Seitz (WS) radius, , is always a n increasing function of the polarization i.e., the
volume of a bulk metal always increases as increases, and the rate of
increasing is higher for higher electron density metals. Using the SJM along
with the local spin density approximation, we have also calculated the
equilibrium WS radius, , of spherical jellium clusters, at
which the pressure on the cluster with given numbers of total electrons, ,
and their spin configuration vanishes. Our calculations f or Cs, Na,
and Al clusters show that as a function of behaves
differently depending on whether corresponds to a closed-shell or an
open-shell cluster. For a closed-shell cluster, it is an increasing function of
over the whole range , whereas in open-shell clusters
it has a decreasing behavior over the range , where
is a polarization that the cluster has a configuration consistent
with Hund's first rule. The resu lts show that for all neutral clusters with
ground state spin configuration, , the inequality always holds (self-compression) but, at some
polarization , the inequality changes the direction
(self-expansion). However, the inequality
always holds and the equality is achieved in the limit .Comment: 7 pages, RevTex, 10 figure
Bicomplex neural networks with hypergeometric activation functions
Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In this paper, we present a BCCNN, and we apply it to a classification task involving the colorized version of the well-known dataset MNIST. Besides the novelty of considering bicomplex numbers, our CNN considers an activation function a Bessel-type function. As we see, our results present better results compared with the one where the classical ReLU activation function is considered.publishe
Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings
We investigate the low-temperature properties of the one-dimensional spin-1
Heisenberg model with geometric fluctuations induced by aperiodic but
deterministic coupling distributions, involving two parameters. We focus on two
aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is
to understand how these geometric fluctuations modify the physics of the
(gapped) Haldane phase, which corresponds to the ground state of the uniform
spin-1 chain. We make use of different adaptations of the strong-disorder
renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in
the study of random spin chains, supplemented by quantum Monte Carlo and
density-matrix renormalization-group numerical calculations, to study the
nature of the ground state as the coupling modulation is increased. We find no
phase transition for the Fibonacci chain, while we show that the 6-3 chain
exhibits a phase transition to a gapless, aperiodicity-dominated phase similar
to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is
verified for random spin-1 chains, we show that different adaptations of the
SDRG scheme may lead to different qualitative conclusions about the nature of
the ground state in the presence of aperiodic coupling modulations.Comment: Accepted for publication in Physical Review
The Anomalous Hall effect in re-entrant AuFe alloys and the real space Berry phase
The Hall effect has been studied in a series of AuFe samples in the
re-entrant concentration range, as well as in the spin glass range. The data
demonstrate that the degree of canting of the local spins strongly modifies the
anomalous Hall effect, in agreement with theoretical predictions associating
canting, chirality and a real space Berry phase. The canonical parametrization
of the Hall signal for magnetic conductors becomes inappropriate when local
spins are canted.Comment: 4 pages, 1 eps figur
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