Related papers: A Small Parameter Method for Few-Body Problems
Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate {\gamma}-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method…
This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
Since the pioneering work of L\"uscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While…
We present a general approach for modelling the small-scale suppression in the linear matter power spectrum induced by the presence of non-cold dark matter. We show that the new parametrisation accurately describes a large variety of…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
Recently, we introduced a solution to the quantum marginal problem relevant to two-dimensional quantum many-body systems [I. H. Kim, Phys. Rev. X, 11, 021039]. One of the conditions was that the marginals are internally translationally…
Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the…
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated…
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…
New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…
Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…