1,797 research outputs found
Spectrum of bound fermion states on vortices in He-B
We study subgap spectra of fermions localized within vortex cores in
He-B. We develop an analytical treatment of the low-energy states and
consider the characteristic properties of fermion spectra for different types
of vortices. Due to the removed spin degeneracy the spectra of all singly
quantized vortices consist of two different anomalous branches crossing the
Fermi level. For singular and vortices the anomalous branches are
similar to the standard Caroli-de Gennes -Matricon ones and intersect the Fermi
level at zero angular momentum yet with different slopes corresponding to
different spin states. On the contrary the spectral branches of nonsingular
vortices intersect the Fermi level at finite angular momenta which leads to the
appearance of a large number of zero modes, i.e. energy states at the Fermi
level. Considering the , and vortices with superfluid cores we
show that the number of zero modes is proportional to the size of the vortex
core.Comment: 6 pages, 1 figur
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
Incomplete Transition Complexity of Basic Operations on Finite Languages
The state complexity of basic operations on finite languages (considering
complete DFAs) has been in studied the literature. In this paper we study the
incomplete (deterministic) state and transition complexity on finite languages
of boolean operations, concatenation, star, and reversal. For all operations we
give tight upper bounds for both description measures. We correct the published
state complexity of concatenation for complete DFAs and provide a tight upper
bound for the case when the right automaton is larger than the left one. For
all binary operations the tightness is proved using family languages with a
variable alphabet size. In general the operational complexities depend not only
on the complexities of the operands but also on other refined measures.Comment: 13 page
Monopoles and fractional vortices in chiral superconductors
We discuss two exotic objects, which must be experimentally identified in
chiral superfluids and superconductors. These are (i) the vortex with
fractional quantum number (N=1/2 in chiral superfluids, and N=1/2 and N=1/4 in
chiral superconductors), which plays the part ofthe Alice string in
relativistic theories; and (ii) the hedgehog in the l-field, which is the
counterpart of the Dirac magnetic monopole. These objects of different
dimensions are topologically connected. They form the combined object which is
called nexus in relativistic theories. In chiral superconductors the nexus has
magnetic charge emanating radially from the hedgehog, while the half-quantum
vortices play the part of the Dirac string. Each of them supplies the
fractional magnetic flux to the hedgehog, representing 1/4 of the
"conventional" Dirac string. We discuss the topological interaction of the
superconductor's nexus with the `t Hooft-Polyakov magnetic monopole, which can
exist in GUT. The `t Hooft-Polyakov magnetic monopole and the hedgehog with the
same magnetic charge are topologically confined by a piece of the Abrikosov
vortex. Other properties of half-quantum vortices and monopoles are discussed
as well, including fermion zero modes.Comment: RevTex file, 8 pages, 6 Figures, prepared for Proc. Nat. Ac. Sc. US,
typos corrected, one Figure added (the loop trapping fractional flux in
chiral superconductors
Fermions on half-quantum vortex
The spectrum of the fermion zero modes in the vicinity of the vortex with
fractional winding number is discussed. This is inspired by the observation of
the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev.
Lett. 76 (1996) 1336). The fractional value of the winding number leads to the
fractional value of the invariant, which describes the topology of the energy
spectrum of fermions. This results in the phenomenon of the "half-crossing":
the spectrum approaches zero but does not cross it, being captured at the zero
energy level. The similarity with the phenomenon of the fermion condensation is
discussed.Comment: In revised version the discussion is extended and 4 references are
added. The paper is accepted for publication in JETP Letters. 10 pages, LaTeX
file, 3 figures are available at
ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96004.p
Effective spacetime and Hawking radiation from moving domain wall in thin film of 3He-A
An event horizon for "relativistic" fermionic quasiparticles can be
constructed in a thin film of superfluid 3He-A. The quasiparticles see an
effective "gravitational" field which is induced by a topological soliton of
the order parameter. Within the soliton the "speed of light" crosses zero and
changes sign. When the soliton moves, two planar event horizons (black hole and
white hole) appear, with a curvature singularity between them. Aside from the
singularity, the effective spacetime is incomplete at future and past
boundaries, but the quasiparticles cannot escape there because the
nonrelativistic corrections become important as the blueshift grows, yielding
"superluminal" trajectories. The question of Hawking radiation from the moving
soliton is discussed but not resolved.Comment: revtex file, 4 pages, 2 figures, submitted to JETP Let
Vortex Mass in BCS systems: Kopnin and Baym-Chandler contributions
The Kopnin mass and the Baym-Chandler mass of the vortex have the same
origin. Both represent the mass of the normal component trapped by the vortex.
The Kopnin mass of the vortex is formed by quasiparticles localized in the
vicinity of the vortex. In the superclean limit it is calculated as linear
response exactly in the same way as the density of the normal component is
calculated in homogeneous superfluid. The Baym-Chandler mass is the
hydrodynamical (associated) mass trapped by vortex. It is analogous to the
normal component formed by inhomogeneities, such as pores and impurities. Both
contributions are calculated for the generic model of the continuous vortex
core.Comment: revtex file, 3 pages, 1 figure. Initially appeared as Comment to the
paper by E.B. Sonin et al "Vortex motion in charged and neutral superfluids:
A hydrodynamic approach" (Phys. Rev. B 57, 575 (1998)). The calculation of
the backflow mass is adde
The Need for Effective Early Behavioral Family Interventions for Children with Attention Deficit Hyperactivity Disorder (ADHD)
There is a pressing need for the development of effective early family intervention programs for children showing Attention Deficit Hyperactivity Disorder (ADHD) behaviours with Conduct Disorder (CD) or Oppositional Defiant Disorder (ODD) behaviours. Previous research has indicated that children with ADHD are at risk of developing comorbid CD or ODD behaviours. In addition, it has been shown that ODD or CD behaviours in childhood tend to persist and to have adverse effects on later social adjustment. However, ODD or CD behaviours are not necessary concomitants of ADHD, and it has been demonstrated that behavioural intervention can have both short- and long term beneficial effects for children showing early signs of ODD or CD behaviours. In short term, behavioural family interventions may be able to reduce oppositional behaviour, particularly in the preschool years. In the long term, early intervention has shown to reduce the incidence of later antisocial behaviour in children at risk for this developmental trajectory. In this paper, it will be argued that behavioural family interventions have not been effectively utilised or promulgated in the community for children with ADHD despite the demonstrated efficacy of these types of interventions. A model of a multilevel system of intervention that can be tailored to the individual family’s needs is presented
Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation
Directed graphs (DG), interpreted as state transition diagrams, are
traditionally used to represent finite-state automata (FSA). In the context of
formal languages, both FSA and regular expressions (RE) are equivalent in that
they accept and generate, respectively, type-3 (regular) languages. Based on
our previous work, this paper analyzes effects of graph manipulations on
corresponding RE. In this present, starting stage we assume that the DG under
consideration contains no cycles. Graph manipulation is performed by deleting
or inserting of nodes or arcs. Combined and/or multiple application of these
basic operators enable a great variety of transformations of DG (and
corresponding RE) that can be seen as mutants of the original DG (and
corresponding RE). DG are popular for modeling complex systems; however they
easily become intractable if the system under consideration is complex and/or
large. In such situations, we propose to switch to corresponding RE in order to
benefit from their compact format for modeling and algebraic operations for
analysis. The results of the study are of great potential interest to mutation
testing
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