9,963 research outputs found
Chiral CP^2 skyrmions in three-band superconductors
It is shown that under certain conditions, three-component superconductors
(and in particular three-band systems) allow stable topological defects
different from vortices. We demonstrate the existence of these excitations,
characterized by a topological invariant, in models for three-component
superconductors with broken time reversal symmetry. We term these topological
defects "chiral skyrmions", where "chiral" refers to the fact that
due to broken time reversal symmetry, these defects come in inequivalent left-
and right-handed versions. In certain cases these objects are energetically
cheaper than vortices and should be induced by an applied magnetic field. In
other situations these skyrmions are metastable states, which can be produced
by a quench. Observation of these defects can signal broken time reversal
symmetry in three-band superconductors or in Josephson-coupled bilayers of
and s-wave superconductors.Comment: minor presentation changes; replaced journal version; 30 pages, 21
figure
Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems
We analyze the superconducting instabilities in the vicinity of the
quantum-critical point of an inversion symmetry breaking order. We first show
that the fluctuations of the inversion symmetry breaking order lead to two
degenerate superconducting (SC) instabilities, one in the -wave channel, and
the other in a time-reversal invariant odd-parity pairing channel (the simplest
case being the same as the of He-B phase). Remarkably, we find that unlike
many well-known examples, the selection of the pairing symmetry of the
condensate is independent of the momentum-space structure of the collective
mode that mediates the pairing interaction. We found that this degeneracy is a
result of the existence of a conserved fermionic helicity, , and the two
degenerate channels correspond to even and odd combinations of SC order
parameters with . As a result, the system has an enlarged symmetry
, with each corresponding to one value of
the helicity . Because of the enlarged symmetry, this system admits
exotic topological defects such as a fractional quantum vortex, which we show
has a Majorana zero mode bound at its core. We discuss how the enlarged
symmetry can be lifted by small perturbations, such as the Coulomb interaction
or Fermi surface splitting in the presence of broken inversion symmetry, and we
show that the resulting superconducting state can be topological or trivial
depending on parameters. The symmetry is restored at the
phase boundary between the topological and trivial SC states, and allows for a
transition between topologically distinct SC phases without the vanishing of
the order parameter. We present a global phase diagram of the superconducting
states and discuss possible experimental implications.Comment: 14 pages, 5 figures, to match the published versio
Review of Some Promising Fractional Physical Models
Fractional dynamics is a field of study in physics and mechanics
investigating the behavior of objects and systems that are characterized by
power-law non-locality, power-law long-term memory or fractal properties by
using integrations and differentiation of non-integer orders, i.e., by methods
of the fractional calculus. This paper is a review of physical models that look
very promising for future development of fractional dynamics. We suggest a
short introduction to fractional calculus as a theory of integration and
differentiation of non-integer order. Some applications of
integro-differentiations of fractional orders in physics are discussed. Models
of discrete systems with memory, lattice with long-range inter-particle
interaction, dynamics of fractal media are presented. Quantum analogs of
fractional derivatives and model of open nano-system systems with memory are
also discussed.Comment: 38 pages, LaTe
Diffusive approximation of a time-fractional Burger's equation in nonlinear acoustics
A fractional time derivative is introduced into the Burger's equation to
model losses of nonlinear waves. This term amounts to a time convolution
product, which greatly penalizes the numerical modeling. A diffusive
representation of the fractional derivative is adopted here, replacing this
nonlocal operator by a continuum of memory variables that satisfy local-in-time
ordinary differential equations. Then a quadrature formula yields a system of
local partial differential equations, well-suited to numerical integration. The
determination of the quadrature coefficients is crucial to ensure both the
well-posedness of the system and the computational efficiency of the diffusive
approximation. For this purpose, optimization with constraint is shown to be a
very efficient strategy. Strang splitting is used to solve successively the
hyperbolic part by a shock-capturing scheme, and the diffusive part exactly.
Numerical experiments are proposed to assess the efficiency of the numerical
modeling, and to illustrate the effect of the fractional attenuation on the
wave propagation.Comment: submitted to Siam SIA
Analysis of fractional hybrid differential equations with impulses in partially ordered Banach algebras
In this paper, we investigate a class of fractional hybrid differential equations with impulses, which can be seen as nonlinear differential equations with a quadratic perturbation of second type and a linear perturbation in partially ordered Banach algebras. We deduce the existence and approximation of a mild solution for the initial value problems of this system by applying Dhage iteration principles and related hybrid fixed point theorems. Compared with previous works, we generalize the results to fractional order and extend some existing conclusions for the first time. Meantime, we take into consideration the effect of impulses. Our results indicate the influence of fractional order for nonlinear hybrid differential equations and improve some known results, which have wider applications as well. A numerical example is included to illustrate the effectiveness of the proposed results
Action principles for higher and fractional spin gravities
We review various off-shell formulations for interacting higher-spin systems
in dimensions 3 and 4. Associated with higher-spin systems in spacetime
dimension 4 is a Chern-Simons action for a superconnection taking its values in
a direct product of an infinite-dimensional algebra of oscillators and a
Frobenius algebra. A crucial ingredient of the model is that it elevates the
rigid closed and central two-form of Vasiliev's theory to a dynamical 2-form
and doubles the higher-spin algebra, thereby considerably reducing the number
of possible higher spin invariants and giving a nonzero effective functional
on-shell. The two action principles we give for higher-spin systems in 3D are
based on Chern-Simons and BF models. In the first case, the theory we give
unifies higher-spin gauge fields with fractional-spin fields and an internal
sector. In particular, Newton's constant is related to the coupling constant of
the internal sector. In the second case, the BF action we review gives the
fully nonlinear Prokushkin-Vasiliev, bosonic equations for matter-coupled
higher spins in 3D. We present the truncation to a single, real matter field
relevant in the Gaberdiel-Gopakumar holographic duality. The link between the
various actions we present is the fact that they all borrow ingredients from
Topological Field Theory. It has bee conjectured that there is an underlying
and unifying 2-dimensional first-quantised description of the previous
higher-spin models in 3D and 4D, in the form of a Cattaneo-Felder-like
topological action containing fermionic fields.Comment: 41+1 pages. References added and reorganized, corrected typos, last
paragraph of section 2 re-written. Contribution to the proceedings of the
International Workshop on Higher Spin Gauge Theories (4-6 November 2015,
Singapore
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