15,650 research outputs found
Localized solutions of Lugiato-Lefever equations with focused pump
Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D)
accurately describe the dynamics of optical fields in pumped lossy cavities
with the intrinsic Kerr nonlinearity. The external pump is usually assumed to
be uniform, but it can be made tightly focused too -- in particular, for
building small pixels. We obtain solutions of the LL equations, with both the
focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes
supported by the localized pump. In the 1D setting, we first develop a simple
perturbation theory, based in the sech ansatz, in the case of weak pump and
loss. Then, a family of exact analytical solutions for spatially confined modes
is produced for the pump focused in the form of a delta-function, with a
nonlinear loss (two-photon absorption) added to the LL model. Numerical
findings demonstrate that these exact solutions are stable, both dynamically
and structurally (the latter means that stable numerical solutions close to the
exact ones are found when a specific condition, necessary for the existence of
the analytical solution, does not hold). In 2D, vast families of stable
confined modes are produced by means of a variational approximation and full
numerical simulations.Comment: 26 pages, 9 figures, accepted for publication in Scientific Report
Localized modes in quasi-2D Bose-Einstein condensates with spin-orbit and Rabi couplings
We consider a two-component pancake-shaped, i.e., effectively two-dimensional
(2D), Bose-Einstein condensate (BEC) coupled by the spin-orbit (SO) and Rabi
terms. The SO coupling adopted here is of the mixed Rashba-Dresselhaus type.
For this configuration, we derive a system of two 2D nonpolynomial
Schr\"odinger equations (NPSEs), for both attractive and repulsive interatomic
interactions. In the low- and high-density limits, the system amounts to
previously known models, namely, the usual 2D Gross-Pitaevskii equation, or the
Schr\"odinger equation with the nonlinearity of power 7/3. We present simple
approximate localized solutions, obtained by treating the SO and Rabi terms as
perturbations. Localized solutions of the full NPSE system are obtained in a
numerical form. Remarkably, in the case of the attractive nonlinearity acting
in free space (i.e., without any 2D trapping potential), we find parameter
regions where the SO and Rabi couplings make 2D fundamental solitons
dynamically stable.Comment: 8 pages, 9 figures - Physical Review A, in pres
Design sensitivity analysis of nonlinear structural response
A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use
K\"all\'en-Lehmann representation of noncommutative quantum electrodynamics
Noncommutative (NC) quantum field theory is the subject of many analyses on
formal and general aspects looking for deviations and, therefore, potential
noncommutative spacetime effects. Within of this large class, we may now pay
some attention to the quantization of NC field theory on lower dimensions and
look closely at the issue of dynamical mass generation to the gauge field. This
work encompasses the quantization of the two-dimensional massive quantum
electrodynamics and three-dimensional topologically massive quantum
electrodynamics. We begin by addressing the problem on a general dimensionality
making use of the perturbative Seiberg-Witten map to, thus, construct a general
action, to only then specify the problem to two and three dimensions. The
quantization takes place through the K\"all\'en-Lehmann spectral representation
and Yang-Feldman-K\"all\'en formulation, where we calculate the respective
spectral density function to the gauge field. Furthermore, regarding the photon
two-point function, we discuss how its infrared behavior is related to the term
generated by quantum corrections in two dimensions, and, moreover, in three
dimensions, we study the issue of nontrivial {\theta}-dependent corrections to
the dynamical mass generation
Deformations of special geometry: in search of the topological string
The topological string captures certain superstring amplitudes which are also
encoded in the underlying string effective action. However, unlike the
topological string free energy, the effective action that comprises
higher-order derivative couplings is not defined in terms of duality covariant
variables. This puzzle is resolved in the context of real special geometry by
introducing the so-called Hesse potential, which is defined in terms of duality
covariant variables and is related by a Legendre transformation to the function
that encodes the effective action. It is demonstrated that the Hesse potential
contains a unique subsector that possesses all the characteristic properties of
a topological string free energy. Genus contributions are constructed
explicitly for a general class of effective actions associated with a
special-K\"ahler target space and are shown to satisfy the holomorphic anomaly
equation of perturbative type-II topological string theory. This identification
of a topological string free energy from an effective action is primarily based
on conceptual arguments and does not involve any of its more specific
properties. It is fully consistent with known results. A general theorem is
presented that captures some characteristic features of the equivalence, which
demonstrates at the same time that non-holomorphic deformations of special
geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement
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