Few-Body Systems最新文献

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.

The charm (D) and charm-strange ((D_s)) mesons are investigated in a variational scheme using Gaussian trial wave functions. The Hamiltonian contains Song and Lin potential with a constant term dependent on radial and orbital quantum numbers. The Gaussian wave function used has a dependence on radial distance r, radial quantum number n, orbital quantum number l and a trial parameter (mu ). The obtained spectra of D and (D_s) mesons are in good agreement with other theoretical models and available experimental masses. The mass spectra of D and (D_s) mesons are also used to plot Regge trajectories in the (J, (M^2)) and ((n_r), (M^2)) planes. In (J, (M^2)) plane, both natural and unnatural parity states of D and (D_s) mesons are plotted. The trajectories are parallel and equidistant from each other. The two-body strong decays of D and (D_s) are analyzed in the framework of heavy quark effective theory using computed masses. The strong decay widths are given in terms of strong coupling constants. These couplings are also estimated by comparing them with available experimental values for observed states. Also, the partial decay width ratios of different states are analyzed and used to suggest assignments to the observed states. We have assigned the spin-parity to newly observed (D^*_{s2}(2573)) as the strange partner of (D^*_2(2460)) identified as (1^3P_2), (D_1^*(2760)) and (D^*_{s1}(2860)) as (1^3D_1), (D^*_3(2750)) and (D^*_{s3}(2860)) as (1^3D_3), (D_2(2740)) as (1D_2), (D_0(2550)) as (2^1S_0), (D^*_1(2660)) and (D^*_{s1}(2700)) as (2^3S_1), (D^*_J(3000)) as (2^3P_0), (D_J(3000)) as (2P_1), (D^*_2(3000)) as (1^3F_2) states.

In this work, we investigate the mass spectra of all-charm ((cc{bar{c}}{bar{c}})) and doubly strange- doubly charm ((ss{bar{c}}{bar{c}})) tetraquark states using the framework of Regge phenomenology. Employing a quasi-linear Regge trajectory ansatz, we derive linear and quadratic mass inequalities for hadrons, which provide constraints on the masses of tetraquark states. We estimate the range of ground state masses of (cc{bar{c}}{bar{c}}) tetraquarks and determine the Regge slope parameters by fitting the corresponding ((J, M^2)) trajectories. These parameters are then utilized to predict the mass spectra of orbital excited states of both (cc{bar{c}}{bar{c}}) and (ss{bar{c}}{bar{c}}) systems in the ((J, M^2)) plane. Furthermore, we extend our analysis to radial excitations by exploring Regge trajectories in the ((n, M^2)) plane. The obtained mass predictions are compared with existing theoretical results from various models. Additionally, we discuss the possible identification of the experimentally observed (psi (4660)) and (chi _{c0}(4700)) resonances as tetraquark candidates. The results presented in this study offer useful benchmarks for future experimental investigations and may assist in the spin-parity assignment of exotic hadronic states. Our findings contribute to a deeper understanding of multiquark dynamics and the spectroscopy of exotic hadrons within the framework of Quantum Chromodynamics.

In this study, we revisit the Schwinger–Dyson equation for the electron propagator in QED in three- and four-space–time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking which demands a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the said Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schrödinger-like equation with an auxiliary potential barrier (well) subjected to boundary conditions for both high and low momenta. Then, the dynamical mass is associated with the zero mode of the corresponding Schrödinger-like operator and adheres to the Miransky scaling law, as expected.

We investigate three-body recombination of helium and hydrogen atoms at cold collision energies, adopting the hyperspherical adiabatic formulation. By taking into account non-rotating ((J=0)) and rotating ((J>0)) states, we calculate the rates for the recombination processes (^4)He+(^4)He+X(rightarrow ^4)He(_2)+X (X=(^1)H, (^2)H, (^3)H and (^3)He), up to 0.1 Kelvin. In addition, we compute the collision induced dissociation rates for the same three-body systems.