相关论文: Example of two different potentials which have pra…
Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H = -Delta + vf(x), where the potential shape f(x) is symmetric and monotone increasing for x > 0, and the coupling parameter v is positive. If the 'kinetic…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact…
New families of time-dependent potentials related with the stationary singular oscillator are introduced. This is achieved after noticing that a non stationary quantum invariant can be constructed for the singular oscillator. Such invariant…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…
We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…
We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…
We propose a procedure based on phase equivalent chains of Darboux transformations to generate local potentials satisfying the radial Schr\"odinger equation and sharing the same scattering data. For potentials related by a chain of…
Elegant and mathematically rigorous methods of the quantum inverse theory are difficult to put into practice because there is always some lack of needful input information. In this situation, one may try to construct a reference potential,…
Large-scale simulations of plastic deformation and phase transformations in alloys require reliable classical interatomic potentials. We construct an embedded-atom method potential for niobium as the first step in alloy potential…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
Phase shifts for $\alpha$ + nucleon scattering generated by a multichannel RGM model of the five-nucleon system are subjected to iterative-perturbative ``mixed-case" inversion for energies below the reaction threshold. The resulting…
An overview of the authors results is given. Property C for ODE is defioned, It is proved that the pair of Sturm-Liouville operators has property C. This property is applied to many inverse problems. Some well-known results, such as…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a…
Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive…
This work presents exchange potentials for specific orbitals calculated by inverting Hartree-Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies upon the substitution of…
At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…
Finding a Z-eigenpair of a symmetric tensor is equivalent to finding a KKT point of a sphere constrained minimization problem. Based on this equivalency, in this paper, we first propose a class of iterative methods to get a Z-eigenpair of a…