Search results for "Nonlinear"
showing 10 items of 3684 documents
Algebraic Quantization, Good Operators and Fractional Quantum Numbers
1995
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…
Post-Newtonian constraints onf(R)cosmologies in metric and Palatini formalism
2005
We compute the complete post-Newtonian limit of both the metric and Palatini formulations of $f(R)$ gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian $f(R)$ must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian $f(R)$ must be almost linear in $R$ and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot b…
Cosmic microwave background anisotropy: deviations from Gaussianity caused by non-linear gravity
2002
Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N-body simulations - in aCDM cosmology - are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combined with the potential approximation to calculate the statistical moments of the CMB anisotropies produced by non-linear gravity. Some of these moments are computed and the resulting values are different from those corresponding to Gaussianity.
Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism
2019
We derive an effective Hamiltonian system describing the low-energy dynamics of circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry arguments, we model (anti)skyrmion dynamics through a finite set of coupled, canonically conjugated, collective coordinates. The resulting theoretical description is independent of both micromagnetic details as well as any specificity in the ansatz of the skyrmion profile. Based on the Hamiltonian structure, we derive a general description for breathing dynamics of (anti)skyrmions in the limit of radius much larger than the domain wall width. The effective energy landscape reveals two qualitatively different types of breathing behavior. Fo…
Modeling harmonic generation by a degenerate two-level atom
1996
An analytical theory of the generation of high-order harmonics of laser radiation has been developed on the basis of a two-level model atom with degenerate levels. Among other parameters, onset, width, and cutoff of the plateau in the harmonic spectrum are obtained in simple analytical forms that connect the basic problem parameters and permit a transparent interpretation of the mechanism underlying the spectrum formation for this specific case. Selected numerical calculations are reported to corroborate the analytical findings and to investigate other harmonic-spectrum features.
Thermal solitons along wires with flux-limited lateral exchange
2021
We obtain some exact solutions in the context of solitons, for heat conduction with inertia along a cylinder whose heat exchange with the environment is a non-linear function of the difference of temperatures of the cylinder and the environment, due to a flux-limiter behavior of the exchange. We study the consequences of heat transfer and information transfer along the wire, and we compare the situation with analogous solitons found in nonlinear lateral radiative exchange studied in some previous papers. We also find further exact solutions in terms of Weierstrass elliptic functions for the sake of completeness.
Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons
2001
Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.
Integration of massive states as contractions of non linear sigma-models
2005
We consider the contraction of some non linear sigma models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N=1 and N=2 theories, as they appear in certain low energy effective supergravity actions with mass deformations. The contraction procedure is shown to describe the integrating out of massive modes in the presence of interactions, as it happens in many supergravity models after spontaneous supersymmetry breaking.
Reflection equations and q-Minkowski space algebras
1994
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties with respect the quantum Lorentz group action in a straightforward way.
Correspondence between modified gravity and general relativity with scalar fields
2018
We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a different scalar field Lagrangian. Our analysis considers examples with a single and $N$ real scalar fields, described either by canonical Lagrangians or by generalized functions of the kinetic and potential terms. In particular, we consider several explicit examples involving $f(R)$ theories and the Eddington-inspired Born-Infeld gravity model, coupled to different scalar field Lagrangians. We show how the nonlinearities of the gravitational sector of these t…