1,593 research outputs found
k-Spectra of weakly-c-Balanced Words
A word is a scattered factor of if can be obtained from by
deleting some of its letters. That is, there exist the (potentially empty)
words , and such that and
. We consider the set of length- scattered
factors of a given word w, called here -spectrum and denoted
\ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w)
for binary strictly balanced and, respectively, -balanced words , i.e.,
words over a two-letter alphabet where the number of occurrences of each letter
is the same, or, respectively, one letter has -more occurrences than the
other. In particular, we consider the question which cardinalities n=
|\ScatFact_k(w)| are obtainable, for a positive integer , when is
either a strictly balanced binary word of length , or a -balanced binary
word of length . We also consider the problem of reconstructing words
from their -spectra
Motion of vortices in ferromagnetic spin-1 BEC
The paper investigates dynamics of nonsingular vortices in a ferromagnetic
spin-1 BEC, where spin and mass superfluidity coexist in the presence of
uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based
on hydrodynamics following from the Gross-Pitaevskii theory. Cores of
nonsingular vortices are skyrmions with charge, which is tuned by uniaxial
anisotropy and can have any fractal value between 0 and 1. There are
circulations of mass and spin currents around these vortices. The results are
compared with the equation of vortex motion derived earlier in the
Landau-Lifshitz-Gilbert theory for magnetic vortices in easy-plane
ferromagnetic insulators. In the both cases the transverse gyrotropic force
(analog of the Magnus force in superfluid and classical hydrodynamics) is
proportional to the charge of skyrmions in vortex cores.Comment: 19 pages, 2 figures, to be published in the special issue of Fizika
Nizkikh Temperatur dedicated to A.M.Kosevich. arXiv admin note: substantial
text overlap with arXiv:1801.0109
Resonant Tunneling through Multi-Level and Double Quantum Dots
We study resonant tunneling through quantum-dot systems in the presence of
strong Coulomb repulsion and coupling to the metallic leads. Motivated by
recent experiments we concentrate on (i) a single dot with two energy levels
and (ii) a double dot with one level in each dot. Each level is twofold
spin-degenerate. Depending on the level spacing these systems are physical
realizations of different Kondo-type models. Using a real-time diagrammatic
formulation we evaluate the spectral density and the non-linear conductance.
The latter shows a novel triple-peak resonant structure.Comment: 4 pages, ReVTeX, 4 Postscript figure
Quantum circuits with uniformly controlled one-qubit gates
Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some
result
Stability of multi-electron bubbles in liquid helium
The stability of multi-electron bubbles in liquid helium is investigated
theoretically. We find that multi-electron bubbles are unstable against fission
whenever the pressure is positive. It is shown that for moving bubbles the
Bernoulli effect can result in a range of pressures over which the bubbles are
stable.Comment: 7 pages, 5 figure
On the effect of the thermal gas component to the stability of vortices in trapped Bose-Einstein condensates
We study the stability of vortices in trapped single-component Bose-Einstein
condensates within self-consistent mean-field theories--especially we consider
the Hartree-Fock-Bogoliubov-Popov theory and its recently proposed gapless
extensions. It is shown that for sufficiently repulsively interacting systems
the anomalous negative-energy modes related to vortex instabilities are lifted
to positive energies due to partial filling of the vortex core with
noncondensed gas. Such a behavior implies that within these theories the vortex
states are eventually stable against transfer of condensate matter to the
anomalous core modes. This self-stabilization of vortices, shown to occur under
very general circumstances, is contrasted to the predictions of the
non-self-consistent Bogoliubov approximation, which is known to exhibit
anomalous modes for all vortex configurations and thus implying instability of
these states. In addition, the shortcomings of these approximations in
describing the properties of vortices are analysed, and the need of a
self-consistent theory taking properly into account the coupled dynamics of the
condensate and the noncondensate atoms is emphasized.Comment: 8 page
Comparison of mean-field theories for vortices in trapped Bose-Einstein condensates
We compute structures of vortex configurations in a harmonically trapped
Bose-Einstein condensed atom gas within three different gapless self-consistent
mean-field theories. Outside the vortex core region, the density profiles for
the condensate and the thermal gas are found to differ only by a few percent
between the Hartree-Fock-Bogoliubov-Popov theory and two of its recently
proposed gapless extensions. In the core region, however, the differences in
the density profiles are substantial. The structural differences are reflected
in the energies of the quasiparticle states localized near the vortex core.
Especially, the predictions for the energy of the lowest quasiparticle
excitation differ considerably between the theoretical models investigated.Comment: 4 pages, 2 figure
Topological superfluid He-B: fermion zero modes on interfaces and in the vortex core
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
topology allows us to determine generic features of their fermionic spectrum,
which are robust to perturbation and interaction. We discuss the nodeless 3D
system, such as superfluid He-B, vacuum of Dirac fermions, and relativistic
singlet and triplet supercondutors which may arise in quark matter. The
systems, which have nonzero value of topological invariant, have gapless
fermions on the boundary and in the core of quantized vortices. We discuss the
index theorem which relates fermion zero modes on vortices with the topological
invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices,
Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi,
Finlan
Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement
Recently, it has been shown that every recursively enumerable language can be
generated by a scattered context grammar with no more than three nonterminals.
However, in that construction, the maximal number of nonterminals
simultaneously rewritten during a derivation step depends on many factors, such
as the cardinality of the alphabet of the generated language and the structure
of the generated language itself. This paper improves the result by showing
that the maximal number of nonterminals simultaneously rewritten during any
derivation step can be limited by a small constant regardless of other factors
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