Three-body Interatomic Interactions Research Articles

Chirped nonlinear waves in the cubic-quintic distributed nonlinear Schrödinger equation with external trap, self-steepening and self-frequency shift

A cubic-quintic inhomogeneous nonautonomous nonlinear Schrödinger (NLS) equation with an external trap, self-steepening, and self-frequency shift that models the transmission of nonlinear waves in nonautonomous inhomogeneous systems is considered. The integrability conditions under which the equation is converted into the standard NLS equation are obtained and a variety of nonlinear wave solutions with nonlinear chirping such as one-soliton solution, two-soliton solution, Akhmediev breather (AB) solution, Ma breather (MB) solution, as well as first- and second-order rogue wave (RW) solution are reported. We show how various parameters of either the model equation or the solutions may affect the nature of nonlinear waves with their frequency chirps propagating in nonautonomous inhomogeneous systems modeled by the NLS equation under consideration. The density profiles of nonlinear waves obtained from all these solutions are analyzed. These solutions are used for investigating analytically the dynamics of nonlinear waves in Bose-Einstein condensates (BECs) with both two- and three-body interatomic interactions when the gain/loss of atoms is taken into consideration. Considering BEC systems with time-independent trap frequency, we show that under a constant gain/loss parameter, the trap parameter can be used to convert triplet second-order RWs into either doublet second-order RWs or a composite of one bright solitary wave and a doublet second-order RWs. Also, our results reveal that for BECs with constant trap frequency under kink-like gain/loss parameter, the trap parameter can be used to convert (i) triplet second-order RWs into single second-order RWs, and (ii) two-soliton into doublet rogue wave. The family of chirped nonlinear wave solutions presented in this work may prove significance for designing the manipulation and transmission of nonlinear waves. Also, the found here results may provide possibilities to manipulate experimentally some nonlinear waves such as rogue waves or two-soliton in BEC systems.

Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients* *The first author, EK dedicates this work to the memory of his Father-in-law, His Majesty Sado Jean Le Prince, Deceased on the June 2nd, 2020

In this work, we consider the generalized cubic–quintic dissipative Gross–Pitaevskii equation, which governs the dynamics of matter wave solitons in Bose–Einstein condensates with two- and three-body interatomic interactions in a spatiotemporal-dependent dissipative potential consisting of parabolic, linear, and complex terms. By using the ansatz method, the modulational instability and gray, kink, and bright soliton solutions are presented under certain parametric conditions. We found that the complex potential, related to the feeding or the loss of atoms by the condensates seriously modifies the instability and stability domain, while the linear potential has not effect on the stability of the system. With the use of exact analytical soliton-like solutions, we investigate analytically the solitons control system, and the results show that the soliton control system may relax the limitations to parametric conditions. We found that the motion of matter wave solitons in the systems can be manipulated by controlling both the external harmonic and linear trapping potentials. We have established that the amplitude of the matter wave solitons keep no change in propagating in the system though the total number of the condensate atoms decreases (increases) when the condensate losses (gains) atoms. We also showed that the three-body interatomic interactions is responsible of the soliton compression. Our results also revealed that the found exact soliton-like solutions can be used to describe the compression of matter wave solitons in BEC system with loss of atoms.

Matter-wave solitons of Bose–Einstein condensates with time-dependent complex potentials

To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system and present an explicit expression for the growth rate of a purely growing MI. Effects of the parabolic background potential, as well as of the linear potential, the gain/loss parameter, and the two- and three-body interatomic interactions on the MI are investigated. We show how the feeding/loss parameter can be well used to control the instability of the system. The analytical resolution of the considered GP equation leads to exact bright, dark and kink solitary wave solutions which are used to investigate analytically the dynamics of matter-wave solitons in BECs under consideration. These analytical investigations show that the amplitude and the motion of bright, dark and kink solitary waves depend on the strengths of the two- and three-body interatomic interactions, as well as on the strengths of the external trapping potential and the parameter of the gain/loss of atoms in the condensate.

Solitons in multi-body interactions for a fully modulated cubic–quintic Gross–Pitaevskii equation

• Dynamics of solitons in a fully modulated cubic–quintic Gross–Pitaevskii equation is analyzed. • Role of quintic parameter on the size of wave numbers of carrier and envelope is analyzed. • Lax-pair for the model with varying coefficients and external potential is given. • Regions of modulational instability and linear and nonlinear stabilities are investigated. A phase imprint approach is applied to a cubic Gross–Pitaevskii equation (GPE) in order to obtain a modified non-autonomous derivative cubic–quintic nonlinear GPE with fully variable coefficients. This model describes the dynamics of condensates in Bose–Einstein condensates, with both two- and three-body interatomic interactions with an external potential when the coefficient of the dispersion term is constant. This model is also applicable to fiber optics media in the absence of external potential. We show that this modified GPE model has a Lax-pair when all of its coefficients depend on time. However, the external potential depends on both the time and space variables. We obtain two classes of exact analytical solutions. These classes of solutions contain four different types of solitary-like wave solutions in the form of kink, anti-kink, bright, dark solitary, and periodic wave solutions. We reveal the effects of a quintic term on wave numbers, for both the carrier and envelope waves. Stability analysis is carried out, and conditions on parameters that determine regions with linear stability are discussed. Graphical analysis of some solutions are presented.

Effects of three-body interactions on the instabilities and self-oscillations of the four-wave mixing in Bose–Einstein condensates

In this paper, we analyze and discuss instabilities and self-oscillations of four-wave mixing in two-component Bose–Einstein condensates with two- and three-body interatomic interactions. The model is very accurately described in the mean-field approximation by the cubic–quintic Gross–Pitaevskii equation. The relation between the input and output field intensities is multivalued and the effects of the quintic nonlinearity on the self-oscillations of the system are studied. We have also found that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases with the increase of the intensity of the probe beam. We have shown that the three-body interatomic interactions enhance this saturated value.

Mechanical Characterization of Boron-Nitride Nanoribbons via Nonlinear Structural Mechanics

In the present paper, the tensile mechanical behavior of different sized, almost squared shaped, boron nitride nanoribbons is numerically investigated and predicted by using a structural mechanics approach based on the use of appropriate nonlinear potential functions concerning both two-body and three-body interatomic interactions appearing within their nanostructure. According to the proposed method, appropriate spring elements are combined in nanoscale in order to simulate the interatomic interactions appearing within boron-nitride nanostructure. The dimensions of boron-nitride nanoribbons as well as the shape of their edges, which may be armchair or zigzag, have influence on the overall behavior of the nanoribbons. Therefore, the study focuses on the prediction of tensile stress-strain behavior of boron-nitride nanoribbons of different sizes and edge shapes as well as on the estimation of significant corresponding material properties such as Young’s modulus, tensile strength, tensile failure strain and tensile toughness. The numerical results, which are compared with corresponding data given in the open literature where possible, demonstrate thoroughly the important influence of size and chirality of a narrow boron nitride monolayer on its mechanical behavior.

Dynamics of matter-wave condensates with time-dependent two- and three-body interactions trapped by a linear potential in the presence of atom gain or loss.

Bose-Einstein condensates with time varying two- and three-body interatomic interactions, confined in a linear potential and exchanging atoms with the thermal cloud are investigated. Using the extended tanh-function method with an auxiliary equation, i.e., the Lenard equation, many exact solutions describing the dynamics of matter-wave condensates are derived. An important issue is the time management of the cubic and the quintic nonlinearities by tuning the rate of exchange of atoms between the condensate and the thermal background. In addition, adjusting the strength of the linear potential, the rate of exchange of atoms, and many other free parameters allow one to control many features of the condensate such as its height, width, position, velocity, acceleration, and its direction, respectively. Full numerical solutions corroborate the analytical predictions.

Molecular-dynamics simulation of structural and thermodynamic properties of ternary alloy ZnSxSe1-x

Molecular dynamics simulation is being widely applied in condensed matter physics, rather Monte Carlo simulation, whenever the dynamic properties are of much interest. Particulary of equilibrium and non-equilibrium phenomena, transport phenomena, diffusivity, specific heat and phase transitions etc. Therefore, we have used this method, in order to obtain more informations about the structural, elastic and thermodynamic properties of ZnS0.25Se0.75, ZnS0.5Se0.5 and ZnS0.75Se0.25. We have also predicted the disorder effect (bowing parameter). We have used molecular simulation coupled with the empirical interatomic potentials on the Tersoff which include the three-body interatomic interactions. We have proposed empirical potentials of Tersoff parameters of ZnSxSe1-x for x = 0.25, x = 0.50 and x = 0.75. We have tested the validity of our fitting of empirical interatomic potentials parameters by calculating the physical properties. Overall, the results are in good agreement with other calculations.

Effects of three-body interactions in the parametric and modulational instabilities of Bose–Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic–quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.

A variational approach to the modulational instability of a Bose–Einstein condensate in a parabolic trap

By means of the time-dependent variational approach, we study the modulational instability of Bose–Einstein condensates (BECs), with both two- and three-body interatomic interactions, trapped in an external parabolic potential. Within this framework, we derive and analyse ordinary differential equations for the explicit time evolution of the amplitude and phase of modulational perturbation. The effect of the trapping coefficients as well as the quintic nonlinear interaction on the dynamics of the BEC are examined. Numerical simulations are carried out in order to support our theoretical findings.

Modulational instability of a trapped Bose-Einstein condensate with two- and three-body interactions

We investigate analytically and numerically the modulational instability of a Bose-Einstein condensate with both two- and three-body interatomic interactions and trapped in an external parabolic potential. Analytical investigations performed lead us to establish an explicit time-dependent criterion for the modulational instability of the condensate. The effects of the potential as well as of the quintic nonlinear interaction are studied. Direct numerical simulations of the Gross-Pitaevskii equation with two- and three-body interactions describing the dynamics of the condensate agree with the analytical predictions.

Monte Carlo and Molecular Dynamics Simulations of Liquid Semiconductor Surfaces

ABSTRACTWe have numerically studied the surface tension and surface profiles of several liquid semiconductors, including Si, Ge, GaAs, CdTe, and their alloys, as a function of temperature and concentration. Two kinds of simulations have been carried out: direct free-energy calculations using Monte Carlo methods, and force summations using molecular dynamics. We use empirical two- and three-body interatomic interactions based on the form originally proposed by Stillinger and Weber for Si, in conjunction with simulation cell sizes ranging from 216 to as large as 8000 atoms and several novel numerical techniques including a direct calculation of the surface entropy. In the case of alloys, we find a striking segregation of the low-surface-tension component to the surface even when the alloy components are miscible at all concentrations.