Few-Body Systems最新文献

Using representation–theoretic techniques associated with the (mathfrak {su}(1,1)) symmetry algebra, we construct Perelomov coherent states for the Dunkl–Klein–Gordon equation in its canonical form, which is free of first–order Dunkl derivatives. Our analysis is restricted to the even–parity sector and to the regime where the curvature constant ( R ) is much smaller than the system’s kinetic energy. The equation under consideration emerges from a matrix–operator framework based on Dirac gamma matrices and a universal length scale that encodes the curvature of space via the Dunkl operator, thereby circumventing the need for spin connections in the Dirac equation.

In the present work, we predict the existence of new types of hydrogenlike matter, including hydrogenlike atoms ((pi ^+e^-), (K^+e^-), (D^+e^-)), hydrogenlike molecular ions ((pi ^+pi ^+e^-), (K^+K^+e^-), (D^+D^+e^-)) and hydrogenlike molecules ((pi ^+pi ^+e^-e^-), (K^+K^+e^-e^-), (D^+D^+e^-e^-)). By solving the Schrödinger equation, the binding energy of hydrogenlike atoms is obtained as (E_n=-frac{1}{2n^2}). For hydrogenlike molecular ions and molecules, the variational method is employed to calculate the binding energies, i.e., (E_+=-0.587) and (E_0=-1.139) for hydrogenlike molecular ions and molecules, respectively. And the bond lengths for hydrogenlike molecular ions and molecules are also calculated, whose values are 2.003 and 1.414, respectively. Here all the quantities are in atomic units for convenience. In addition, the strong interaction between the two constituent mesons is considered in our calculations, where we find that its influence on the hydrogenlike molecular ions and molecules can be neglected. Comparisons of hydrogenlike molecular ion and molecule with the systems governed by the strong interaction are made, which suggests the possible existence of doubly heavy triquark, hidden heavy-flavor tetraquarks and doubly heavy tetraquarks. Hopefully, these types of matter would be observed in the future with the improvement of accuracy in the high energy physical experiments.

We investigate the plasma sscreening effects on the van der Waals two-body dispersion coefficients, C(_{textrm{6}}), for interactions among heliumlike atoms (Z(=)2-10), using highly accurate correlated exponential wave functions. Two different plasma models, namely, the Debye plasma model and quantum plasma model are considered. The Debye-Hückel potential is used to model the Debye plasma environment, and the exponential cosine screened Coulomb potential is used to model the quantum plasma environment. The dispersion coefficients C(_{textrm{6}})for interactions among screened-heliumlike atoms (Z(=)2-10) in their ground states for different screening parameters, are reported for the first time in the literature.

In this work, we solve the nonrelativistic symplectic Schrödinger-type equation for a two-body system within the framework of symplectic quantum mechanics. By employing a Lie algebraic approach, we obtain an explicit solution for the wave function in phase space. Subsequently, we derive the corresponding Wigner function and analyze its behavior. As an application, we investigate the heavy quark-antiquark system, specifically the (coverline{c}) meson, which interacts through a linear term of the Cornell potential model. The Wigner function is studied to describe the ground state of the meson. Furthermore, our results indicate that small variations in kinetic momentum significantly affect the maximum possible relative quark-antiquark separation q in (textrm{GeV}^{-1}). This suggests the existence of an upper limit for the Wigner function curves of the heavy quark-antiquark pair, dependent on the kinetic energy, as illustrated in our graphical analysis. These findings align with previous results in the literature. We also emphasize that the methodology adopted for the study of this equation is based on the theory of Lie groups for differential equations, and with application in the calculation of conservation laws using the Noether theorem.

The behavior of Bose-Einstein condensates (BECs) near the Feshbach resonance is a challenging research area. We present a correlated many-body approach to calculate the atom number fluctuation at large scattering length when the trapped bosons interact via the realistic two-body van der Waals potential. Atom number fluctuation is the key property of strongly interacting finite-sized quantum systems. It is theoretically challenging when the particles become highly correlated. We observe that fluctuation is enhanced in the strongly interacting limit for the bosons trapped in a spherical potential. Introducing the anharmonicity, the atom number fluctuation and critical temperature of the condensate depend regourously on the number of particle. In the anharmonic trap, the trap geometry and interaction play an intricate role exhibiting maximal fluctuation at intermediate particle number.

In this work, we investigate electron energy spectra and localization in a three-dimensional harmonium system using the shifted 1/N-expansion method. Our results show that increasing confinement strength (upomega ) raises energy levels and reduces equilibrium interelectron distances, as stronger confinement forces electrons into tighter spatial regions. In the strong-correlation limit (upomega rightarrow 0), we confirm the formation of a Wigner molecule. Additionally, we establish the transition from the Wigner molecule regime to a strongly confined state where quantum confinement suppresses correlation effects. Our results further show that energy levels increase by increasing the principal quantum number (n), while centrifugal effects lead to a slight reduction in energy levels with increasing angular momentum number ((ell )). These results enhance our understanding of electron correlation effects in confined quantum systems and have potential applications in nanophysics and quantum computing.

We present a comprehensive analysis of four-body scattering in one-dimensional (1D) quantum systems using the adiabatic hyperspherical representation (AHR). Focusing on dimer-dimer collisions between two species of fermions interacting via the sinh-cosh potential, we implement the slow variable discretization (SVD) method to overcome numerical challenges posed by sharp avoided crossings in the potential curves. Our numerical approach is benchmarked against exact analytical results available in integrable regimes, demonstrating excellent agreement. We further explore non-integrable regimes where no analytical solutions exist, revealing novel features such as resonant enhancement of the scattering length associated with tetramer formation. These results highlight the power and flexibility of the AHR+SVD framework for accurate few-body scattering calculations in low-dimensional quantum systems, and establish a foundation for future investigations of universal few-body physics in ultracold gases.

The study of exotic multi-quark states has garnered significant attention recently, particularly in heavy-quark dynamics within quantum chromodynamics. We perform a comprehensive spectroscopic analysis of multi-heavy pentaquark states with four and five heavy quarks having configurations (QQQQ{bar{q}}), and (QQQQ{bar{Q}}), considering spin-parity assignments (J^P = 1/2^-), (3/2^-), and (5/2^-). Using an extended Gursey-Radicati formalism, by incorporating spin-dependent interactions, we calculated their mass spectra for possible quantum numbers. The modification incorporates effective mass contributions and hyperfine interactions to improve the predictive power of these hadronic states. The calculated mass spectra are compared with existing theoretical predictions, which exhibit a strong dependence on the interplay between spin interactions and color configurations, shedding light on the binding mechanism within these multi-heavy multiquark systems. To gain further insight into their stability and decay properties, we investigated their potential production modes from B-hadron decays. Our analysis identifies dominant strong decay channels, providing critical theoretical benchmarks for distinguishing these states in future LHCb or EIC experiments. This study offers new insights into the role of heavy-quark dynamics in exotic hadron spectroscopy, serving as a stringent test for effective QCD-based models and lattice QCD predictions.

We present a detailed variational study of the helium atom using compact, generalized exponential basis functions (GEFs) that incorporate non-integer radial powers and adjustable exponential decay parameters. These trial wave functions, originally introduced by Koga and Kanayama, offer improved flexibility for describing electron behavior near the nucleus and at large distances. By optimizing the variational parameters a, b, and x, we construct wave functions that closely approximate the Hartree-Fock (HF) ground state using only a single basis term. We evaluate key expectation values, including (langle hbox {r}rangle ), (langle 1/textrm{r}rangle ), (langle hbox {r}_{12}rangle ), (langle hbox {r}_{<}rangle ), and (langle hbox {r}_{>}rangle ), and analyze the effects of radial power and decay parameters on kinetic, nuclear attraction, and electron-electron repulsion energies. Our results demonstrate that the total energy can be lowered to within 0.20 millihartree of the HF limit, matching the performance of larger Slater-type orbital expansions with far fewer parameters. We further investigate the influence of wave function parameters on the nuclear cusp and radial probability density. The findings highlight the utility of GEFs in compact atomic modeling, offering both computational efficiency and near-HF-limit accuracy, with significant pedagogical value for quantum chemistry instruction.

Supersymmetric quantum mechanics (SUSY-QM) provides a powerful framework for analyzing exactly solvable quantum systems. This study extends this formalism to a class of hyperbolic potentials within position-dependent mass (PDM) systems, which are crucial for modeling graded semiconductor heterostructures and other effective quantum theories. While the constant-mass case is confirmed to be exactly solvable, introducing a position-dependent mass presents a fundamental theoretical challenge. The nonlinear coupling between the spectral parameters and the superpotential generally breaks the standard shape-invariance condition, preventing a general analytical solution through the standard SUSY hierarchy. Our central result is the derivation, by strictly enforcing shape invariance as a constraint, of a unique and exactly solvable scenario. This process self-consistently identifies a specific, compatible pair of mass profile (Mleft( xright) ) and potential( Vleft( xright) ). This pair emerges not as an arbitrary choice but as the fundamental solution that preserves the underlying supersymmetric symmetry, highlighting that shape invariance itself acts as a selection rule dictating which mass profiles permit exact solvability for a given potential type. This solvable model establishes a critical analytical benchmark for future studies on more complex, non-shape-invariant PDM systems. It demonstrates a robust methodology for identifying exact solutions in generalized quantum contexts, consolidating the role of SUSY-QM in tackling the challenges of position-dependent mass.