Solenoidal Lipschitz truncation for parabolic PDE's

We consider functions $u\in L^\infty(L^2)\cap L^p(W^{1,p})$ with $1<p<\infty$ on a time space domain. Solutions to non-linear evolutionary PDE's typically belong to these spaces. Many applications require a Lipschitz approximation $u_\lambda$ of $u$ which coincides with $u$ on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids in [DRW10]. Since ${\rm div} u_\lambda=0$, we are able to work in the pressure free formulation, which heavily simplifies the proof. We also provide a simplified approach to the stationary solenoidal Lipschitz truncation of [BDF12]

Generalized Zero Range Potentials and Multi-Channel Electron-Molecule Scattering

A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. Spherical functions basis expansion of the potentials introduces partial amplitudes and corresponding radial functions. The approach is generalized to multi-channel case by a matrix formulation in which a state vector component is associated with a scattering channel. The zero-range potentials naturally enter the scheme when the class of operators of multiplication is widen to distributions. %Analog of multipolar expansion is treated. Spin variables, o Oscillations and rotations are incorporated into the scheme.Comment: 11 pages, 1 figure, CEPAS2 con

2s Hyperfine Structure in Hydrogen Atom and Helium-3 Ion

The usefulness of study of hyperfine splitting in the hydrogen atom is limited on a level of 10 ppm by our knowledge of the proton structure. One way to go beyond 10 ppm is to study a specific difference of the hyperfine structure intervals 8 Delta nu_2 - Delta nu_1. Nuclear effects for are not important this difference and it is of use to study higher-order QED corrections.Comment: 10 pages, presented at Hydrogen Atom II meeting (2000

Ultrafast dynamics of coherences in the quantum Hall system

Using three-pulse four-wave-mixing optical spectroscopy, we study the ultrafast dynamics of the quantum Hall system. We observe striking differences as compared to an undoped system, where the 2D electron gas is absent. In particular, we observe a large off-resonant signal with strong oscillations. Using a microscopic theory, we show that these are due to many-particle coherences created by interactions between photoexcited carriers and collective excitations of the 2D electron gas. We extract quantitative information about the dephasing and interference of these coherences.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let

Evaluation of the self-energy correction to the g-factor of S states in H-like ions

A detailed description of the numerical procedure is presented for the evaluation of the one-loop self-energy correction to the $g$-factor of an electron in the $1s$ and $2s$ states in H-like ions to all orders in $Z\alpha$.Comment: Final version, December 30, 200

Correlated many-body treatment of Breit interaction with application to cesium atomic properties and parity violation

Corrections from Breit interaction to basic properties of atomic 133Cs are determined in the framework of third-order relativistic many-body perturbation theory. The corrections to energies, hyperfine-structure constants, off-diagonal hyperfine 6S-7S amplitude, and electric-dipole matrix elements are tabulated. It is demonstrated that the Breit corrections to correlations are comparable to the Breit corrections at the Dirac-Hartree-Fock level. Modification of the parity-nonconserving (PNC) 6S-7S amplitude due to Breit interaction is also evaluated; the resulting weak charge of $^{133}$Cs shows no significant deviation from the prediction of the standard model of elementary particles. The neutron skin correction to the PNC amplitude is also estimated to be -0.2% with an error bound of 30% based on the analysis of recent experiments with antiprotonic atoms. The present work supplements publication [A. Derevianko, Phys. Rev. Lett. 85, 1618 (2000)] with a discussion of the formalism and provides additional numerical results and updated discussion of parity violation.Comment: 16 pages; 5 figs; submitted to Phys. Rev.

Role of Present and Future Atomic Parity Violation Experiments in Precision Electroweak Tests

Recent reanalyses of the atomic physics effects on the weak charge in cesium have led to a value in much closer agreement with predictions of the Standard Model. We review precision electroweak tests, their implications for upper bounds on the mass of the Higgs boson, possible ways in which these bounds may be circumvented, and the requirements placed upon accuracy of future atomic parity violation experiments by these considerations.Comment: 10 pages, LaTeX, 1 figure, to be submitted to Physical Review D, new data on neutrino deep inelastic scattering include

A dressing of zero-range potentials and electron-molecule scattering problem at Ramsauer-Townsend minimum

A dressing technique is used to improve zero range potential (ZRP) model. We consider a Darboux transformation starting with a ZRP, the result of the "dressing" gives a potential with non-zero range that depends on a seed solution parameters. Concepts of the partial waves and partial phases for non-spherical potential are used in order to perform Darboux transformation. The problem of scattering on the regular X$_{\hbox{n}}$ and YX$_{\hbox{n}}$ structures is studied. The results of the low-energy electron-molecule scattering on the dressed ZRPs are illustrated by model calculation for the configuration and parameters of the silane ($\hbox{SiH}_4$) molecule. \center{Key words: low-energy scattering, multiple scattering, Ramsauer-Townsend minimum, silane, zero range potential.Comment: 13 pages, 1 figur

Can the magnetic moment contribution explain the A_y puzzle?

We evaluate the full one-photon-exchange Born amplitude for $Nd$ scattering. We include the contributions due to the magnetic moment of the proton or neutron, and the magnetic moment and quadrupole moment of the deuteron. It is found that the inclusion of the magnetic-moment interaction in the theoretical description of the $Nd$ scattering observables cannot resolve the long-standing $A_y$ puzzle.Comment: 7 pages, 2 Postscript figures; to appear in Phys.Rev.

On the Detectability of the Hydrogen 3-cm Fine Structure Line from the EoR

A soft ultraviolet radiation field, 10.2 eV < E <13.6 eV, that permeates neutral intergalactic gas during the Epoch of Reionization (EoR) excites the 2p (directly) and 2s (indirectly) states of atomic hydrogen. Because the 2s state is metastable, the lifetime of atoms in this level is relatively long, which may cause the 2s state to be overpopulated relative to the 2p state. It has recently been proposed that for this reason, neutral intergalactic atomic hydrogen gas may be detected in absorption in its 3-cm fine-structure line (2s_1/2 -> 2p_3/2) against the Cosmic Microwave Background out to very high redshifts. In particular, the optical depth in the fine-structure line through neutral intergalactic gas surrounding bright quasars during the EoR may reach tau~1e-5. The resulting surface brightness temperature of tens of micro K (in absorption) may be detectable with existing radio telescopes. Motivated by this exciting proposal, we perform a detailed analysis of the transfer of Lyman beta,gamma,delta,... radiation, and re-analyze the detectability of the fine-structure line in neutral intergalactic gas surrounding high-redshift quasars. We find that proper radiative transfer modeling causes the fine-structure absorption signature to be reduced tremendously to tau< 1e-10. We therefore conclude that neutral intergalactic gas during the EoR cannot reveal its presence in the 3-cm fine-structure line to existing radio telescopes.Comment: 7 pages, 4 figures, MNRAS in press; v2. some typos fixe