Related papers: A Pedestrian Introduction to Gamow Vectors
We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states.…
We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle…
We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time…
The theoretical evaluation of major nuclear structure effects on the asymmetry of allowed Gamow-Teller beta-decay rates in light mirror nuclei is presented. The calculations are performed within the shell model, using empirical…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…
We analyze the one dimensional scattering produced by all variations of the P\"oschl-Teller potential, i.e., potential well, low and high barriers. We show that the P\"oschl-Teller well and low barrier potentials have no resonance poles,…
For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residues. Beautiful hidden structures can be revealed by its…
We analyze the detailed time dependence of the wave function $\psi(x,t)$ for one dimensional Hamiltonians $H=-\partial_x^2+V(x)$ where $V$ (for example modeling barriers or wells) and $\psi(x,0)$ are {\em compactly supported}. We show that…
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\sigma$, and the resonances of…
We study a planar magnetic Schr\"odinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on…
We present an $\mathcal{O}(\alpha)$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\beta$ decays. We find that \textit{a priori} contributions arise from the photonic vertex correction and $\gamma W$ box…
The study of open quantum systems (OQSs), i.e., systems interacting with an environment, impacts our understanding of exotic nuclei in low-energy nuclear physics, hadrons, cold-atom systems, or even noisy intermediate-scale quantum…
The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…
A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes…
The time evolution of plane waves in the presence of a 1-dimensional square quantum barrier is considered. Comparison is made between the cases of an infinite and a cut-off (shutter) initial plane wave. The difference is relevant when the…
We will discuss the asymptotic behaviour of the eigenvalues of Schr\"{o}dinger operator with a matrix potential defined by Neumann boundary condition in $L_2^m(F)$, where $F$ is $d$-dimensional rectangle and the potential is a $m \times m$…
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
The Gamow shell model is utilized to describe nuclear observables of the weakly bound and resonance isotonic states of $^{16}$O at proton drip-line. It is hereby shown that the presence of continuum coupling leads to complex Coulomb…