Related papers: Quantum resonances and partial differential equati…
In general, discrete eigenstates such as resonances are represented by poles of the scattering amplitude, analytically continued to the complex energy plane. In multi-channel scattering, however, the Riemann surface becomes more…
What effect do particle-emitting resonances have on the scattering cross section? What physical considerations are necessary when modelling these resonances? These questions are important when theoretically describing scattering experiments…
A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances…
We investigate the formation of resonances in the P33 partial wave with the emphasis on possible emergence of dynamically generated quasi-bound states as a consequence of a strong $p$-wave pion attractive interaction in this partial wave,…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
We present a microscopical theory and experimental results concerning resistance resonance in two tunneling coupled quantum wells with different mobilities. The shape of the resonance appears to be sensitive to the small angle scattering…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
We review the analytic results for the phase shifts delta_{l}(k) in non-relativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for…
The quantum resonances of classically chaotic n-disk geometries were studied experimentally utilizing thin 2-D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
In the standard Breit-Wigner approach to scattering the phase shift is to have a form $\tan\delta_{\rm BW} =\Gamma_1/(E_1-E)$ at a real energy resonance. This leads to complex energy poles in the scattering amplitude at $E_{\rm…
We review recent developments on quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogs shows diffusive, localized or critical behavior are considered. These are features that cannot be described by the…
In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in…
We study the isolated resonances occurring in conductance fluctuations of quantum systems with a classically mixed phase space. We demonstrate that the isolated resonances and their scattering states can be associated to eigenstates of the…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
Quantum stochastic operator equations are derived for inter-branch exciton and polariton processes caused by acoustic phonon scattering. The use of a fully quantum model combined with these recently developed techniques predicts the…
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured…
Multiquark resonances are undoubtedly experimentally observed. The number of states and the amount of details on their properties has been growing over the years. It is very recent the discovery of two pentaquarks and the confirmation of…
The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the…
Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling…