Search results for "Mathematical physics"
showing 10 items of 2687 documents
Infrared singularities of scattering amplitudes in perturbative QCD
2009
An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/ep…
Studies of inelastic cross-section in Rb(7S) + Rb(5S) collisions
1996
The cross section σ = (8 ± 4) × 10−15 cm2 was determined for the Rb(7S) + Rb(5S) → Rb(5D) + Rb(5S) excitation energy transfer process, and the quenching cross section σq = (2 ± 1) × 10−14 cm2 for the Rb(5D) state in collisions with ground state Rb atoms. Applying rubidium quasimolecular asymptotic potential curves at relatively large internuclear distances, a qualitative interpretation of the experimental results is presented. It is shown that the quenching of the Rb(5D) atoms in collisions may be explained by a reversed energy pooling process Rb(5D) + Rb(5S) → Rb(5P) + Rb(5P).
Dynamical stabilization of spin systems in time-dependent magnetic fields
2011
The quantum dynamics of a spin system subjected to a Rabi magnetic field configuration modified by a weak oscillating field along the Z-axis is investigated. We show that when the Rabi frequency is appropriately matched with the frequency of the perturbative field, the spin system exhibits a dynamical stabilization phenomenon defined as the tendency to occupy a fixed quantum superposition during a finite period of time.
A calorimeter for the precise determination of the activity of the 144Ce-144Pr anti-neutrino source in the SOX experiment
2018
We describe the design and the performance of a high precision thermal calorimeter, whose purpose was the measurement of the total activity of the 144Ce-144Pr anti-neutrino source of the SOX (Short distance neutrino Oscillation with BoreXino) experiment. SOX aimed at the search for eV-scale sterile neutrinos by means of the Borexino detector at the Laboratori Nazionali del Gran Sasso in Italy and of a very powerful artificial anti-neutrino source located at 8.51 m from the detector center. In order to obtain the required sensitivity, the activity of the source (approximately 150 kCi) had to be known at 1% precision. In this work we report the design of the experimental apparatus and the res…
Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons
2016
Recent numerical relativity simulations within the Einstein--Maxwell--(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordstr\"om black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of the superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these $\textit{unstable}$ solitons leads…
On Green's function for cylindrically symmetric fields of polarized radiation
2009
Analytic expressions for Green's function describing the process of transfer of polarized radiation in homogeneous isotropic infinite medium in case of cylindrical symmetry and nonconservative scattering are obtained. The solution is based on the set of systems of Abel integral equations of the first kind obtained using the principle of superposition, and the known expression of Green's function for radiation fields with plane-parallel symmetry. Eigenvalue decompositions for the corresponding matrices of generalized spherical functions are found. Using this result the systems of Abel integral equations are diagonalized, and the final solution is obtained.
High-voltage monitoring with a solenoid retarding spectrometer at the KATRIN experiment
2014
The KATRIN experiment will measure the absolute mass scale of neutrinos with a sensitivity of m(ν) = 200meV/c(2) by means of an electrostatic spectrometer set close to the tritium β-decay endpoint at 18.6keV. Fluctuations of the energy scale must be under control within ±60mV (±3ppm). Since a precise voltage measurement in the range of tens of kV is on the edge of current technology, a nuclear standard will be deployed additionally. Parallel to the main spectrometer the same retarding potential will be applied to the monitor spectrometer to measure 17.8-keV K-conversion electrons of (83m)Kr. This article describes the setup of the monitor spectrometer and presents its first measurement resu…
High-precision x-ray spectroscopy of highly charged ions with microcalorimeters
2013
The precise determination of the energy of the Lyman α1 and α2 lines in hydrogen-like heavy ions provides a sensitive test of quantum electrodynamics in very strong Coulomb fields. To improve the experimental precision, the new detector concept of microcalorimeters is now exploited for such measurements. Such detectors consist of compensated-doped silicon thermistors and Pb or Sn absorbers to obtain high quantum efficiency in the energy range of 40–70 keV, where the Doppler-shifted Lyman lines are located. For the first time, a microcalorimeter was applied in an experiment to precisely determine the transition energy of the Lyman lines of lead ions at the experimental storage ring at GSI. T…
A Tutorial Approach to the Renormalization Group and the Smooth Feshbach Map
2006
2.1 Relative Bounds on the Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Feshbach Map and Pull-Through Formula . . . . . . . . . . . . . . . . . 4 2.3 Elimination of High-Energy Degrees of Freedom . . . . . . . . . . . . . . . . 5 2.4 Normal form of Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Banach Space of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 The Renormalization Map Rρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Renormalization-scheme ambiguity and perturbation theory near a fixed point
1984
We consider the perturbative calculation of critical exponents in massless, renormalizable theories having a nontrivial fixed point. In conventional perturbation theory, all results depend on the arbitrary renormalization scheme used. We show how to resolve this problem, following the "principle of minimal sensitivity" approach. At least three orders of perturbation theory are required for quantitative results. We give scheme-independent criteria for determining the presence or absence of a fixed point in $n\mathrm{th}$ order, and discuss the conditions under which perturbative results might be reliable. As illustrations we discuss QED with many flavors, and ${({\ensuremath{\varphi}}^{4})}_…