Related papers: Recovery of a quarkonium system from experimental …
It is well known that a potential $q$ of the Sturm-Liouville operator $Ly= -y" +q(x)y$ on the finite interval $[0, \pi]$ can be uniquely recovered by the spectrum $\{\lambda_k\}_1^\infty$ and norming constants $\{\alpha_k\}_1^\infty$ of…
We consider the BVP $-y" + qy = \lambda y$ with $y(0)=y(1)=0$. The inverse spectral problems asks one to recover $q$ from spectral information. In this paper, we present a very simple method to recover a potential by sampling one…
The spectra and decay rates of $c \bar c$ and $b \bar b$ levels are well described, for the most part, by a power-law potential of the form $V(r)=\lambda(r^{\alpha}-1)/\alpha+{\rm const.}$, where $\alpha\simeq 0$. The results of an…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
We reconstruct compactly supported potentials with only half a derivative in $L^2$ from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined…
For a time-independent potential $q\in L^\infty$, consider the source-to-solution operator that maps a source $f$ to the solution $u=u(t,x)$ of $(\Box+q)u=f$ in Euclidean space with an obstacle, where we impose on $u$ vanishing Cauchy data…
A renormalization scheme is suggested where QCD input parameters - quark mass and coupling constant - are expressed in terms of gauge invariant and infrared stable quantities. For the renormalization of coupling constant the quark anomalous…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
We study the problem of recovering a collection of $n$ numbers from the evaluation of $m$ power sums. This yields a system of polynomial equations, which can be underconstrained ($m < n$), square ($m = n$), or overconstrained ($m > n$).…
Using methods previously developed by Kelbg and others for creating effective potentials for electron-ion plasmas, we investigate quarkonium potentials above deconfinement. Using results for the internal energy of a static quark-antiquark…
We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…
Analytic solutions for the energy eigenvalues are obtained from a confined potentials of the form $br$ in 3 dimensions. The confinement is effected by linear term which is a very important part in Cornell potential. The analytic eigenvalues…
We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength r and frequency omega. Starting with the system in the bound state, the survival probability is for small r given by…
The energy eigenvalues with any l-states and mass of heavy quark- antiquark system (quarkonium) are obtained by using Asymptotic Iteration Method in the view of non-relativistic quantum chromodynamics, in which the quarks are considered as…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
In this paper we derive a new recovery procedure for the reconstruction of extended exponential sums of the form $y(t) = \sum_{j=1}^{M} \left( \sum_{m=0}^{n_j} \, \gamma_{j,m} \, t^{m} \right) {\mathrm e}^{2\pi \lambda_j t}$, where the…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
The mystery of the origin of the mass of the elementary particles persists despite the success of quantum field theories to the highest level of accuracy. Renormalization program has been the essential part of the calculation of the…
The entropic approach to dissociation of bound states immersed in strongly coupled systems is developed. In such systems, the excitations of the bound state are often delocalized and characterized by a large entropy, so that the bound state…
Classical $(r,\delta)$-locally recoverable codes are designed for avoiding loss of information in large scale distributed and cloud storage systems. We introduce the quantum counterpart of those codes by defining quantum…