Search results for "classical"
showing 10 items of 2294 documents
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
2015
Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
2015
Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04
Analytic Bergman operators in the semiclassical limit
2018
Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
Dynamics of the scenery flow and geometry of measures
2015
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a n…
Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice
2018
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstra…
Inclusion of a suite of weathering tracers in the cGENIE Earth system model-muffin release v.0.9.23
2021
Abstract. The metals strontium (Sr), lithium (Li), osmium (Os) and calcium (Ca), together with their isotopes, are important tracers of weathering and volcanism – primary processes which shape the long-term cycling of carbon and other biogeochemically important elements at the Earth's surface. Traditionally, because of their long residence times in the ocean, isotopic shifts in these four elements observed in the geologic record are almost exclusively interpreted with the aid of isotope-mixing, tracer-specific box models. However, such models may lack a mechanistic description of the links between the cycling of the four metals to other geochemically relevant elements, particularly carbon, …
Resonances for nonanalytic potentials
2009
We consider semiclassical Schr"odinger operators on $R^n$, with $C^infty$ potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around $R^n$.
Comments on `A new efficient method for calculating perturbation energies using functions which are not quadratically integrable'
1996
The recently proposed method of calculating perturbation energies using a non-normalizable wavefunction by Skala and Cizek is analysed and rigorously proved.
Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model
2013
We consider a two-photon quantum model of radiation–matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system, the explicit construction of two collective radiation modes, one of which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.