Related papers: Electronic Final States in Nuclear $\beta$ Decay: …
Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. Remarkably, these are revealed in one and two electron molecular systems if the realm of the nuclear charge is extended to be…
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…
The collective structure of atomic nuclei intermediate between spherical and quadrupole deformed structure presents challenges to theoretical understanding. However, models have recently been proposed in terms of potentials which are soft…
A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a…
We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the…
In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
Three-parametric family of non-Hermitian but ${\cal PT}-$symmetric six-by-six matrix Hamiltonians $H^{(6)}(x,y,z)$ is considered. The ${\cal PT}-$symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies…
The phenomenon of degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(\lambda)$ the degeneracy occurs at a Kato's exceptional point…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of…
Open systems with gain and loss, described by non-trace-preserving, non-Hermitian Hamiltonians, have been a subject of intense research recently. The effect of exceptional-point degeneracies on the dynamics of classical systems has been…
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the…
We present a new theory describing the variation of electron capture and bound-state $\beta$-decays in atomic ions and (non) local thermodynamic equilibrium ((N)LTE) plasmas. We adopt the Takahashi-Yokoi nuclear model with added corrections…
A simultaneous calculation for the shape evolution and the related spectroscopic properties of the low-lying states, and the $\beta$-decay properties in the even- and odd-mass Ge and As nuclei in the mass $A\approx70-80$ region, within the…
The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $\Delta$-resonance scattering channel. As an extension of effective field theory incorporating the L\"uscher formalism, HEFT…
Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of…
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This…
Quasi-forbidden electronic transitions in atoms and quasi-degenerate vibronic transitions in molecules serve as powerful probes of hypothetical temporal variations of fundamental constants. Computation of the sensitivity of a transition to…