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We consider the description of a Fermi gas of free electrons given by the Boltzmann--Fermi--Dirac equation, and aim at providing a precise mathematical understanding of the Fermi ground state and its first-order approximation of excited…
Fermi's Golden Rule (FGR) is one of the most impactful formulas in quantum mechanics, providing a link between easy-to-measure observables - such as transition rates - and fundamental microscopic properties - such as density of states or…
Total cross sections for electron capture are calculated for collisions of fast protons and alpha-particles with atomic hydrogen. The distorted- wave impulse approximation is applied over the energy range 10-1500 keV/u. State-selective…
We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
Fermi's golden rule underpins the investigation of mobile carriers propagating through various solids, being a standard tool to calculate their scattering rates. As such, it provides a perturbative estimate under the implicit assumption…
We calculate the momentum distribution of the Fermi liquid phase of the homogeneous, two-dimensional electron gas. We show that, close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its…
In this review we consider those processes in condensed matter that involve the irreversible flow of energy between electrons and nuclei that follows from a system being taken out of equilibrium. We survey some of the more important…
The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the…
Recent theories of hot-electron relaxation in dense hydrogen or deuterium are examined in the light of recent molecular-dynamics simulations as well as various theoretical developments within the two-temperature model. The theoretical work…
Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very…
Using dynamical-mean-field theory for clusters, we study the two-dimensional Hubbard model in which electrons are coupled with the orthorhombic lattice distortions through the modulation in the hopping matrix. Instability towards…
We systematically investigate the underlying relations among different levels of approximation for simulating electronic de-excitations, with a focus on modeling X-ray emission spectroscopy (XES). Using Fermi's golden rule and explicit…
We consider a system consisting of a particle in the harmonic approximation, having frequency $\bar{\omega}$, coupled to a scalar field inside a spherical reflecting cavity of diameter $L$. By introducing {\it dressed} coordinates we define…
A study is made of the behavior of unstable states in simple models which nevertheless are realistic representations of situations occurring in nature. It is demonstrated that a non-exponential decay pattern will ultimately dominate decay…
Out-of-equilibrium electron-gas systems exhibit rich physics, which we explore through three problems. First, we study photoemission from metals, traditionally analyzed in the frequency domain. Unexpectedly, the photoemission rate…
Systems containing few Fermions (e.g., electrons) are of great current interest. Fluorescence occurs when electrons drop from one level to another without changing spin. Only electron gases in a state of equilibrium are considered. When the…
Non-adiabatic decay rates for a radio-frequency dressed magnetic trap are calculated using Fermi's Golden Rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the…
We investigate the existence of the electric field reversal in the negative glow of a dc discharge, its location, the width of the well trapping the electrons, the slow electrons scattering time, and as well the trapping time. Based on a…
The first in m/M and fourth in Z\alpha (pure recoil) correction to a hydrogen energy level is found. This correction comprises two contributions, one coming from the atomic scale, the other from distances of the Compton wavelength order.…