Search results for "Functional analysis"

Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well

2015

Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physically relevant properties of related quantum systems have not yet received due (and scientifically undisputable) coverage in the literature. In the present paper we address Schr\"{o}dinger-type eigenvalue problems for $H=T+V$, where a kinetic term $T=T_m$ is a quasirelativistic energy operator $T_m = \sqrt{-\hbar ^2c^2 \Delta + m^2c^4} - mc^2$ of mass $m\in (0,\infty)$ particle. A potential $V$ we assume to refer to the harmonic confinement or finite well of an arbitrary depth. We analyze spectral solutions of the per…

Ghost spectral function from the spectral Dyson-Schwinger equation

2021

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.

Electromagnetic Transition Rate Measurements in theN=80 Isotone,138Ce

2012

A study of intrinsic state halflife measurements in the N=80 nucleus 138Ce has been made using the 130Te(12C,4n)138Ce fusion evaporation reaction at beam energy of 56 MeV. The fast-timing gamma-ray coincidence method was used with a mixed LaBr3(Ce)-HPGe array to establish the lifetimes of the yrast 6+ state at 2294 keV, the Iπ=5− state at 2218 keV, the Iπ=11+ state at 3943 keV and the 14+ state at that at 5312 keV, all of which are in the sub nanosecond regime. Reduced transition probabilities have been calculated for the electromagnetic decays from these states.

Time-resolved photoabsorption in finite systems: A first-principles NEGF approach

2016

We describe a first-principles NonEquilibrium Green’s Function (NEGF) approach to time-resolved photoabsortion spectroscopy in atomic and nanoscale systems. The method is used to highlight a recently discovered dynamical correlation effect in the spectrum of a Krypton gas subject to a strong ionizing pump pulse. We propose a minimal model that captures the effect, and study the performance of time-local approximations versus time-nonlocal ones. In particular we implement the time-local Hartree-Fock and Markovian second Born (2B) approximation as well as the exact adiabatic approximation within the Time-Dependent Density Functional Theory framework. For the time-nonlocal approximation we ins…

Spectroscopy of exotic states of 13C

2014

The differential cross-sections of the elastic and inelastic 13C + α scattering were measured at E (α) = 65 MeV. The radii of the states: 8.86 (1/2¯), 3.09 (1/2+ ) and 9.90 (3/2¯) MeV were determined by the Modified diffraction model (MDM). The radii of the first two levels are enhanced relatively that of the ground state of 13C, confirming the suggestion that the 8.86 MeV state could be an analogue of the Hoyle state in 12C and the 3.09 MeV state has a neutron halo. No enhancement of the radius of the 9.90 MeV state was observed. peerReviewed

Study of the structure of the Hoyle state by refractive α-scattering

2014

α + 12C elastic and inelastic to the Hoyle state (0+ 2, 7.65 MeV) differential cross-sections were measured at the energies 60 and 65 MeV with the aim of testing the microscopic wave function [1] widely used in modern structure calculations of 12C. Deep rainbow (Airy) minima were observed in all four curves. The minima in the inelastic angular distributions are shifted to the larger angles relatively those in the elastic ones, which testify the radius enhancement of the Hoyle state. In general, the DWBA calculations failed to reproduce the details of the cross sections in the region of the rainbow minima in the inelastic scattering data. However, by using the phenomenological density with r…

Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

2005

We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…

Investigating the large deformation of the 5/2+ isomeric state in Zn73 : An indicator for triaxiality

2018

London equation of state for a quantum-hard-sphere system

1994

The London analytical interpolation equation between zero and packing densities for the ground-state energy of a many-boson hard-sphere system is corrected for the reduced mass of a pair of particles in a ``sphere-of-influence'' picture. It is thus brought into good agreement with computer simulations and with experimental results extrapolated out to close packing.

One-Loop Effective Lagrangian in QED

2020

Our main goal in this section is the derivation of an expression for the effective Lagrangian in one-loop approximation. So let’s start with the vacuum persistence amplitude in presence of an external field: $$\displaystyle \langle 0_+\vert 0_-\rangle ^A = e^{ iW^{(1)}[A]} = e^{i \int d^4x\mathcal {L}^{(1)}(x)} $$