相关论文: Simple Soluble Molecular Ionization Model

Finite symmetry adaptation techniques are applied to the determination of the intensity strength of two-photon transitions for ions with one partly-filled shell nl in crystalline environments of symmetry G. We treat the case of intra-…

In this work, we irradiate a superconducting artificial molecule composed of two coupled tunable transmons with microwave light while monitoring its state via joint dispersive readout. Performing high-power spectroscopy, we observe and…

The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov (NU) method, we have obtained the exact analytical s-wave solutions of the…

We investigate different types of complex soliton solutions with regard to their stability against linear pertubations. In the Bullough-Dodd scalar field theory we find linearly stable complex ${\cal{PT}}$-symmetric solutions and linearly…

Two exactly-solvable confined models of the completely positive oscillator-shaped quantum well are proposed. Exact solutions of the position-dependent mass Schr\"odinger equation corresponding to the proposed quantum well potentials are…

We develop a modified Poisson-Nernst-Planck model which includes both the long-range Coulomb and short-range hard-sphere correlations in its free energy functional such that the model can accurately describe the ion transport in complex…

In this study, we present a quantum-statistical analysis of H$_2$ and LiH diatomic molecules within the Frost--Musulin potential framework. By combining the analytical bound-state approach to the radial Schr\"odinger problem with the…

We study the quantum melting of quasi-one-dimensional lattice models in which the dominant energy scale is given by a repulsive dipolar interaction. By constructing an effective low-energy theory, we show that the melting of crystalline…

An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…

We study an integrable quantum field theory of a single stable particle with an infinite number of resonance states. The exact $S$--matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles…

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting…

We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten…

A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined…

The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…

In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a…

The emergence of conformal states is established for any problem involving a domain of scales where the long-range, SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs…

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe theorem \cite{yamada1,yamada2} and the Feller test for…

This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in $\R^2$. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form…

Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by…