Latest Results for Few-Body Systems

21 November 2024

• The Steepest Slope toward a Quantum Few-Body Solution: Gradient Variational Methods for the Quantum Few-Body Problem

  Abstract

  Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrödinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases.We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.

• Rainbow Gravity Effects on Relativistic Quantum Oscillator Field in a Topological Defect Cosmological Space-Time

  Abstract

  In this paper, we investigate the quantum dynamics of scalar and oscillator fields in a topological defect space-time background under the influence of rainbow gravity’s. The rainbow gravity’s are introduced into the considered cosmological space-time geometry by replacing the temporal part \(dt \rightarrow \frac{dt}{\mathcal {F}(\chi )}\) and the spatial part \(dx^i \rightarrow \frac{dx^i}{\mathcal {H} (\chi )}\) , where \(\mathcal {F}, \mathcal {H}\) are the rainbow functions and \(0 \le \chi =|E|/E_p <1\) is the dimensionless parameter. We derived the radial equation of the Klein–Gordon equation and its oscillator equation under rainbow gravity’s in topological space-time. To obtain eigenvalue of the quantum systems under investigations, we set the rainbow functions \(\mathcal {F}(\chi )=1\) and \(\mathcal {H}(\chi )=\sqrt{1-\beta \,\chi ^p}\) , where \(p=1,2\) . We solve the radial equations through special functions using these rainbow functions and analyze the results. In fact, it is shown that the presence of cosmological constant, the topological defect parameter \(\alpha \) , and the rainbow parameter \(\beta \) modified the energy spectrum of scalar and oscillator fields in comparison to the results obtained in flat space.

• On a Repulsive Short-Range Potential Influence on the Harmonic Oscillator

  Abstract

  We study the influence of a symmetrically spherical potential on the harmonic oscillator. The symmetrically spherical potential consists of a repulsive short-range potential inspired by the power-exponential potential. By dealing with s-wave in the region where the repulsive short-range potential is significant, we show how the energy levels of the three-dimensional harmonic oscillator are modified by the short-range potential influence. Furthermore, we show that a non-null revival time with regard to the s-state exists.