514,082 research outputs found
Affine connections and second-order affine structures
Smooth manifolds have been always understood intuitively as spaces with an
affine geometry on the infinitesimal scale. In Synthetic Differential Geometry
this can be made precise by showing that a smooth manifold carries a natural
structure of an infinitesimally affine space. This structure is comprised of
two pieces of data: a sequence of symmetric and reflexive relations defining
the tuples of mutual infinitesimally close points, called an infinitesimal
structure, and an action of affine combinations on these tuples. For smooth
manifolds the only natural infinitesimal structure that has been considered so
far is the one generated by the first neighbourhood of the diagonal. In this
paper we construct natural infinitesimal structures for higher-order
neighbourhoods of the diagonal and show that on any manifold any symmetric
affine connection extends to a second-order infinitesimally affine structure
Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors
Nonuniform superconducting state due to strong spin magnetism is studied in
two-dimensional type-II superconductors near the second order phase transition
line between the normal and the superconducting states. The optimum spatial
structure of the orderparameter is examined in systems with cylindrical
symmetric Fermi surfaces. It is found that states with two-dimensional
structures have lower free energies than the traditional one-dimensional
solutions, at low temperatures and high magnetic fields. For s-wave pairing,
triangular, square, hexagonal states are favored depending on the temperature,
while square states are favored at low temperatures for d-wave pairing. In
these states, orderparameters have two-dimensional structures such as square
and triangular lattices.Comment: 11 pages (LaTeX, revtex.sty), 3 figures; added reference
The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
In this paper, we present extraordinary algebraic and geometrical structures
for the Hunter-Saxton equation: infinitely many commuting and non-commuting
-independent higher order symmetries and conserved densities. Using a
recursive relation, we explicitly generate infinitely many higher order
conserved densities dependent on arbitrary parameters. We find three Nijenhuis
recursion operators resulting from Hamiltonian pairs, of which two are new.
They generate three hierarchies of commuting local symmetries. Finally, we give
a local recursion operator depending on an arbitrary parameter.
As a by-product, we classify all anti-symmetric operators of a definite form
that are compatible with the Hamiltonian operator
Excitons in T-shaped quantum wires
We calculate energies, oscillator strengths for radiative recombination, and
two-particle wave functions for the ground state exciton and around 100 excited
states in a T-shaped quantum wire. We include the single-particle potential and
the Coulomb interaction between the electron and hole on an equal footing, and
perform exact diagonalisation of the two-particle problem within a finite basis
set. We calculate spectra for all of the experimentally studied cases of
T-shaped wires including symmetric and asymmetric GaAs/AlGaAs and
InGaAs/AlGaAs structures. We study in detail the
shape of the wave functions to gain insight into the nature of the various
states for selected symmetric and asymmetric wires in which laser emission has
been experimentally observed. We also calculate the binding energy of the
ground state exciton and the confinement energy of the 1D quantum-wire-exciton
state with respect to the 2D quantum-well exciton for a wide range of
structures, varying the well width and the Al molar fraction . We find that
the largest binding energy of any wire constructed to date is 16.5 meV. We also
notice that in asymmetric structures, the confinement energy is enhanced with
respect to the symmetric forms with comparable parameters but the binding
energy of the exciton is then lower than in the symmetric structures. For
GaAs/AlGaAs wires we obtain an upper limit for the binding energy
of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that
other materials must be explored in order to achieve room temperature
applications. There are some indications that
InGaAs/AlGaAs might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical
Review
Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity
We study cosmic structures in the quadratic Degenerate Higher Order Scalar
Tensor (qDHOST) model, which has been proposed as the most general
scalar-tensor theory (up to quadratic dependence on the covariant derivatives
of the scalar field), which is not plagued by the presence of ghost
instabilities. We then study a static, spherically symmetric object embedded in
de Sitter space-time for the qDHOST model. This model exhibits breaking of the
Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter
space-time outside, where General Relativity (GR) can be recovered within the
Vainshtein radius. We then look for the conditions on the parameters on the
considered qDHOST scenario which ensure the validity of the Vainshtein
screening mechanism inside the object and the fulfilment of the recent
GW170817/GRB170817A constraint on the speed of propagation of gravitational
waves. We find that these two constraints rule out the same set of parameters,
corresponding to the Lagrangians that are quadratic in second-order derivatives
of the scalar field, for the shift symmetric qDHOST.Comment: 16 page
- …