2,327 research outputs found
Generalized solutions and distributional shadows for Dirac equations
We discuss the application of recent results on generalized solutions to the
Cauchy problem for hyperbolic systems to Dirac equations with external fields.
In further analysis we focus on the question of existence of associated
distributional limits and derive their explicit form in case of free Dirac
fields with regularizations of initial values corresponding to point-like
probability densities
Generalized Fourier Integral Operators on spaces of Colombeau type
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras
are defined. This is based on a theory of generalized oscillatory integrals
(OIs) whose phase functions as well as amplitudes may be generalized functions
of Colombeau type. The mapping properties of these FIOs are studied as the
composition with a generalized pseudodifferential operator. Finally, the
microlocal Colombeau regularity for OIs and the influence of the FIO action on
generalized wave front sets are investigated. This theory of generalized FIOs
is motivated by the need of a general framework for partial differential
operators with non-smooth coefficients and distributional data
Classes of generalized functions with finite type regularities
We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities
Dipole trap model for the metallic state in gated silicon-inversion layers
In order to investigate the metallic state in high-mobility Si-MOS
structures, we have further developed and precised the dipole trap model which
was originally proposed by B.L. Altshuler and D.L. Maslov [Phys. Rev. Lett.\
82, 145 (1999)]. Our additional numerical treatment enables us to drop several
approximations and to introduce a limited spatial depth of the trap states
inside the oxide as well as to include a distribution of trap energies. It
turns out that a pronounced metallic state can be caused by such trap states at
appropriate energies whose behavior is in good agreement with experimental
observations.Comment: 16 pages, 10 figures, submitte
Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields
We investigate the dynamic structure factor of the antiferromagnetic Kitaev
honeycomb model in a magnetic field by applying perturbative continuous unitary
transformations about the high-field limit. One- and two-quasi-particle
properties of the dressed elementary spin flip excitations of the high-field
polarized phase are calculated which account for most of the spectral weight in
the dynamic structure factor. We discuss the evolution of spectral features in
these quasi-particle sectors in terms of one-quasi-particle dispersions,
two-quasi-particle continua, the formation of anti-bound states, and
quasi-particle decay. In particular, a comparably strong spectral feature above
the upper edge of the upmost two-quasi-particle continuum represents three
anti-bound states which form due to nearest-neighbor density-density
interactions.Comment: 14 pages, 10 figure
Ising model in a light-induced quantized transverse field
We investigate the influence of light-matter interactions on correlated quantum matter by studying the paradigmatic Dicke-Ising model. This type of coupling to a confined, spatially delocalized bosonic light mode, such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As a consequence, the symmetry-broken magnetic state breaks down for strong enough light-matter interactions to a paramagnetic state. The nonlocal character of the bosonic mode can change the quantum phase transition in a drastic manner, which we analyze quantitatively for the simplest case of the Dicke-Ising chain geometry. The results show a direct transition between a magnetically ordered phase with zero photon density and a magnetically polarized phase with superradiant behavior of the light. Our predictions are equally valid for the dual quantized Ising chain in a conventional transverse magnetic field
The wave equation on singular space-times
We prove local unique solvability of the wave equation for a large class of
weakly singular, locally bounded space-time metrics in a suitable space of
generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by
our results and some examples added. Conclusion more detailed. Version to
appear in Communications in Mathematical Physic
Isomorphisms of algebras of Colombeau generalized functions
We show that for smooth manifolds X and Y, any isomorphism between the
special algebra of Colombeau generalized functions on X, resp. Y is given by
composition with a unique Colombeau generalized function from Y to X. We also
identify the multiplicative linear functionals from the special algebra of
Colombeau generalized functions on X to the ring of Colombeau generalized
numbers. Up to multiplication with an idempotent generalized number, they are
given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page
- …