Two integrable differential-difference equations derived from NLS-type equation

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted semi-discrete systems are given through Hirota's bilinear method. Elastic and inelastic interaction behavior between two solitons are studied through the asymptotic analysis. Dynamics of two-soliton solutions are shown with graphs.Comment: 17 pages, 10 figure

Inflation coupled to a Gauss-Bonnet term

The newly released Planck CMB data place tight constraints on slow-roll inflationary models. Some of commonly discussed inflationary potentials are disfavored due mainly to the large tensor-to-scalar ratio. In this paper we show that these potentials may be in good agreement with the Planck data when the inflaton has a non-minimal coupling to the Gauss-Bonnet term. Moreover, such a coupling violates the consistency relation between the tensor spectral index and tensor-to-scalar ratio. If the tensor spectral index is allowed to vary freely, the Planck constraints on the tensor-to-scalar ratio are slightly improved.Comment: 7 pages, 2 figures, references adde

Bright-dark soliton solutions to the multi-component AB system

In this paper we investigate the multi-component AB system that comes from the geophysical fluid dynamics. We construct bright-dark soliton solutions through Hirota's bilinear method. For the two-component AB system, asymptotic behaviours of two-soliton solution are obtained and interactions between two bright and two dark solitons are proved to be elastic. Under different parameter conditions, the oblique interactions, bound states of solitons are analyzed in details. Meanwhile, by use of the Pfaffian technique, we present $N$-bright and $N-$dark soliton solutions to the two- and multi-component AB system. The results will be meaningful for the study of vector multi-dark solitons in many physical systems such as nonlinear optics and fluid dynamics

Effective Absorption Enhancement in Small Molecule Organic Solar Cells by Employing Trapezoid Gratings

We demonstrate the optical absorption has been enhanced in the small molecule organic solar cells by employing trapezoid grating structure. The enhanced absorption is mainly attributed to both waveguide modes and surface plasmon modes, which has been simulated by using finite-difference time-domain method. The simulated results show that the surface plasmon along the semitransparent metallic Ag anode is excited by introducing the periodical trapezoid gratings, which induce high intensity field increment in the donor layer. Meanwhile, the waveguide modes result a high intensity field in acceptor layer. The increment of field improves the absorption of organic solar cells, significantly, which has been demonstrated by simulating the electrical properties. The simulated results exhibiting 31 % increment of the short-circuit current has been achieved in the optimized device, which is supported by the experimental measurement. The power conversion efficiency of the grating sample obtained in experiment exhibits an enhancement of 7.7 %

Uncover Topology by Quantum Quench Dynamics

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a fundamentally new, high-precision dynamical approach, revealing topology through the unitary evolution after a quench from a topological trivial initial state with a two-dimensional Chern band realized in an ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics uniquely determines the Chern number for the post-quench band and enables probing the full phase diagram of the band topology with high precision. Besides, we also measure the topological band gap and the domain wall structure dynamically formed in the momentum space during the long-term evolution. Our dynamical approach provides a way towards observing a universal bulk-ring correspondence, and has broad applications in exploring topological quantum matter.Comment: 9 pages, 5 figures for main text and 12 pages for supplementary materia

Ultra-low noise magnetic field for quantum gases

Ultra-low noise magnetic field is essential for many branches of scientific research. Examplesinclude experiments conducted on ultra-cold atoms, quantum simulations, as well as precisionmeasurements. In ultra-cold atom experiments specifically, a bias magnetic field will be oftenserved as a quantization axis and be applied for Zeeman splitting. As atomic states areusually sensitive to magnetic fields, a magnetic field characterized by ultra-low noise as wellas high stability is typically required for experimentation. For this study, a bias magneticfield is successfully stabilized at 14.5G, with the root mean square (RMS) value of the noisereduced to 18.5{\mu}G (1.28ppm) by placing{\mu}-metal magnetic shields together with a dynamicalfeedback circuit. Long-time instability is also regulated consistently below 7{\mu}G. The level ofnoise exhibited in the bias magnetic field is further confirmed by evaluating the coherencetime of a Bose-Einstein condensate characterized by Rabi oscillation. It is concluded thatthis approach can be applied to other physical systems as well.Comment: 7 pages, 5 figure

Nonintegrable Spatial Discrete Nonlocal Nonlinear Schr\"odinger Equation

Integrable and nonintegrable discrete nonlinear Schr\"odinger equations (NLS) are significant models to describe many phenomena in physics. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time and reverse space-time nonlocal integrable equations, including nonlocal NLS, nonlocal sine-Gordon equation and nonlocal Davey-Stewartson equation etc. And, the integrable nonlocal discrete NLS has been exactly solved by inverse scattering transform. In this paper, we study a nonintegrable discrete nonlocal NLS which is direct discretization version of the reverse space nonlocal NLS. By applying discrete Fourier transform and modified Neumann iteration, we present its stationary solutions numerically. The linear stability of the stationary solutions is examined. Finally, we study the Cauchy problem for nonlocal NLS equation numerically and find some different and new properties on the numerical solutions comparing with the numerical solutions of the Cauchy problem for NLS equation

The geometric potential of a double-frequency corrugated surface

For an electron confined to a surface reconstructed by double-frequency corrugations, we give the effective Hamiltonian by the formula of geometric influences, obtain an additive scalar potential induced by curvature that consists of attractive wells with different depth. The difference is generated by the multiple frequency of the double-frequency corrugation. Subsequently, we investigate the effects of geometric potential on the transmission probability, and find the resonant tunneling peaks becoming rapidly sharper and the transmission gaps being substantially widened with increasing the multiple frequency. As a potential application, double-frequency corrugations can be employed to select electrons with particular incident energy, as an electronic switch, which are more effective than a single-frequency ones.Comment: 6 pages, 5 figure

The Dirac Conjecture and the Non-uniqueness of Lagrangian

By adding the total time derivatives of all the constraints to the Lagrangian step by step, we achieve the further work of the Dirac conjecture left by Dirac. Hitherto, the Dirac conjecture is proved completely. It is worth noticing that the addition of the total time derivatives to the Lagrangian can turn up some constraints hiding in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ considers more constraints, and shows symmetries more obviously than the total Hamiltonian $H_T$. In the Lagrangian formalism, we reconsider the Cawley counterexample, and offer an example in which in accordance with its original Lagrangian its extended Hamiltonian is better than its total Hamiltonian.Comment: 6 pages, 0 figure

High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases

We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with topological non-trivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the anti-symmetric Raman lattice structure, and generate the 2D SO coupling with precise inversion and $C_4$ symmetries, leading to considerably enlarged topological regions. The life time of the 2D SO coupled Bose-Einstein condensate reaches several seconds, which enables the exploring of fine tuning interaction effects. These essential advantages of the present new realization open the door to explore exotic quantum many-body effects and non-equilibrium dynamics with novel topology.Comment: 6 pages, 4 figure