Nonlinear tunneling through a strong rectangular barrier

Nonlinear tunneling is investigated by analytically solving the one-dimensional Gross–Pitaevskii equation(GPE)with a strong rectangular potential barrier. With the help of analytical solutions of the GPE, which can be reduced to the solution of the linear case, we find that only the supersonic solution in the downstream has a linear counterpart. A critical nonlinearity is explored as an up limit, above which no nonlinear tunneling solution exists. Furthermore, the density solution of the critical nonlinearity as a function of the position has a step-like structure.     

Analytic Study of a Bose-Einstein Condensate in Waveguide with an Obstacle Potential

We investigate the exact solutions of one-dimensional （1D） time-independent Gross-Pitaevskii equation （GPE）, which governs a Bose-Einstein condensate （BEC） in the magnetic waveguide with a square-Sech potential. Both the bound state and transmission state are found and the corresponding spatial configurations and transport properties of BEC are analyzed. It is shown that the well-known absolute transmission of the linear system can occur in the considered nonlinear system.     

Exact solution of Schrdinger equation with q-deformed quantum potentials using Nikiforov–Uvarov method

In this paper,we present the exact solution of the one-dimensional Schrdinger equation for the q-deformed quantum potentials via the Nikiforov–Uvarov method.The eigenvalues and eigenfunctions of these potentials are obtained via this method.The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed.The PT-symmetry and Hermiticity for these potentials are also discussed.     

Dark Soliton Solutions of Space-Time Fractional Sharma–Tasso–Olver and Potential Kadomtsev–Petviashvili Equations

Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.     

Disassociation of a one-dimensional cold molecule via quantum scattering

Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the inte...     

Interaction solutions for the(2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

This paper aims to search for the solutions of the(2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation. Lump solutions, breather solutions, mixed solutions with solitons,and lump-breather solutions can be obtained from the N-soliton solution formula by using the long-wave limit approach and the conjugate complex method. We use both specific circumstances and general higher-order forms of the hybrid solutions as examples. With the help of maple software, we create density and 3D graphs...     

(n+1)-Dimensional Gravity Duals to Quantum Criticalities with Spontaneous Symmetry Breaking

We reexamine the charged AdS domain wall solution to the Einstein–Abelian–Higgs model proposed by Gubser et al.as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions.We generalize their explorations from(3+1)-dimensions to arbitrary n+1Ds and find that the n+1 5D charged AdS domain walls are unstable against electric perturbations.     

A unified charge-based model for SOI MOSFETs applicable from intrinsic to heavily doped channel

A unified charge-based model for fully depleted silicon-on-insulator (SOI) metal–oxide semiconductor field-effect transistors (MOSFETs) is presented. The proposed model is accurate and applicable from intrinsic to heavily doped channels with various structure parameters. The framework starts from the one-dimensional Poisson–Boltzmann equa- tion, and based on the full depletion approximation, an accurate inversion charge density equation is obtained. With the inversion charge density solution, the unified drain current expression is derived, and a unified terminal charge and intrinsic capacitance model is also derived in the quasi-static case. The validity and accuracy of the presented analytic model is proved by numerical simulations.     

Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass

We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable for the case with time-independence mass.     

Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization

The fermionic and bosonic zero modes of the one-dimensional(1D) interacting Kitaev chain at the symmetric point are unveiled. The many-body structures of the Majorana zero modes in the topological region are given explicitly by carrying out a perturbation expansion up to infinite order. We also give the analytic expressions of the bosonic zero modes in the topologically trivial phase. Our results are generalized to the hybrid fermion system comprised of the interacting Kitaev model and the Su–Schrieffer–Heeger(SSH) model, in which we show that these two types of zero modes can coexist in a certain region of its phase diagram.     

Novel interaction phenomena of the(3+1)-dimensional Jimbo–Miwa equation

In this paper,we give the general interaction solution to the(3+1)-dimensional Jimbo–Miwa equation.The general interaction solution contains the classical interaction solution.As an example,by using the generalized bilinear method and symbolic computation by using Maple software,novel interaction solutions under certain constraints of the(3+1)-dimensional Jimbo–Miwa equation are obtained.Via three-dimensional plots,contour plots and density plots with the help of Maple,the physical characteristics and structures of these waves are described very well.These solutions greatly enrich the exact solutions to the(3+1)-dimensional Jimbo–Miwa equation found in the existing literature.     

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

The current–phase relations of a ring-trapped Bose–Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current–phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current–phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current–phase relation is given by investigating the behavior of soliton solution.     

Nonreciprocal transmission of electromagnetic waves by three-layer magneto-optical mediums

We investigate the non-reciprocal transmission properties of a three-layer structure filled with magneto–optical medium and normal medium. Based on the transfer matrix method, we deduce the total transmission coefficient for a one-dimensional(1 D) structure with anisotropic mediums. When two-side layers with magneto–optical medium loaded in opposite external magnetic field, the time-reversal symmetry of transmission properties will be broken. Our numerical results show that the non-reciprocal transmission properties are influenced by external magnetic fields, incident angle, and thickness of the normal medium layer. Since the non-reciprocal properties can be easily realized and adjusted by the simple structure, such a design has potential applications in integrated circulators and isolators.     

Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique,this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However,when the conditions for boundedness of the perturbed solution are satisfied,then the Bose-Einstein condensates are Lyapunov-stable.     

Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

This paper studies the analytical and semi-analytic solutions of the generalized Calogero–Bogoyavlenskii–Schiff(CBS) equation. This model describes the(2 + 1)–dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave. The extended simplest equation(ESE) method is applied to the model, and a variety of novel solitarywave solutions is given. These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma. The accuracy of the obtained solution is verified using a variational iteration(VI) semi-analytical scheme. The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained. The adopted scheme's performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.     

Experimental observation of topologically protected defect states in silicon waveguide arrays

Photonic waveguide arrays provide a simple and versatile platform for simulating conventional topological systems. Here, we investigate a novel one-dimensional(1D) topological band structure, a dimer chain, consisting of silicon waveguides with alternating self-coupling and inter-coupling. Coupled mode theory is used to study topological features of such a model. It is found that topological invariants of our proposed model are described by the global Berry phase instead of the Berry phase of the upper or lower energy band, which is commonly used in the1 D topological models such as the Su–Schrieffer–Heeger model. Next, we design an array configuration composed of two dimer patterns with different global Berry phases to realize the topologically protected waveguiding. The topologically protected propagation feature is simulated based on the finite-difference time-domain method and then observed in the experiment. Our results provide an in-depth understanding of the dynamics of the topological defect state in a 1D silicon waveguide array, and may provide different routes for on-chip lightwave shaping and routing.     

Analytical Approximate Solution of Schr?dinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary l-State

We present the bound state solution of Schr?dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov–Uvarov method to obtain the energy levels and the corresponding eigenfunction in closed form. We also compute the energy eigenvalues numerically.     

Topological phase in one-dimensional Rashba wire

We study the possible topological phase in a one-dimensional(1D) quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.     

One-dimensional continuous analytic potential solution to generic oxide-silicon-oxide system

A one-dimensional continuous analytic potential solution to a generic oxide--silicon--oxide system is developed. With the analytic solution, the potential distribution in the silicon film is predicted. A physics-based relation between surface potentials is also derived and then applied to the generic oxide--silicon--oxide metal--oxide--semiconductor field-effect transistors (MOSFETs) for the calculation of surface potentials     

THz wave emission from argon in two-color laser field

Terahertz(THz) wave emission from argon atom in a two-color laser pulses is studied numerically by solving the one-dimensional(1D) time-dependent Schr ¨odinger equation. The THz spectra we obtained include both discontinuous and continuum ones. By using the special basis functions that we previously proposed, our analysis points out that the discontinuous and continuum parts are contributed by bound–bound and continuum–continuum transition of atomic energy levels. Although the atomic wave function is strongly dressed during the interaction with laser fields, our identification for the discontinuous part of the THz wave shows that the transition between highly excited bound states can still be well described by the field-free basis function in the tunneling ionization regime.