An exact solution for polaron in the nonlinear lattice in the Su–Schrieffer–Heeger approximation

The exact solution for a polaron in a lattice with cubic nonlinearity is obtained. The electron–phonon interaction is taken into account in the Su–Schrieffer–Heeger approximation. The system of nonlinear differential equations in partial derivatives, obtained in the continuum approximation, is exactly integrable at a certain ratio between the parameters of nonlinearity, α, and the electron–phonon interaction, χ. An approximate solution is obtained for arbitrary values of α and χ. A good agreement between the analytical results with the numerical simulation is observed at not too large values of parameters α and χ, where the continuum approximation is valid. Stable solutions also exist at higher values of these parameters.     

Darboux transformation of the Drinfeld–Sokolov–Satsuma–Hirota system and exact solutions

A Darboux transformation for the Drinfeld–Sokolov–Satsuma–Hirota system of coupled equations is constructed with the aid of gauge transformations between the Lax pairs. As an application, several types of solutions of the Drinfeld–Sokolov–Satsuma–Hirota system are obtained, including soliton solutions, periodic solutions, rational solutions and others.     

The generalized Fresnel–Hadamard complementary transformation for asymmetric beamsplitter

Based on the newly developed parameterized coherent-entangled state representation we propose so-called the generalized Fresnel–Hadamard complementary transformation for asymmetric beamsplitter, which is unitary. The new unitary operator plays the role of both Fresnel transformation for a₁ sin θ ? a₂ cos θ and Hadamard transformation for a₁ cos θ + a₂ sin θ, respectively. Physically, a₁ sin θ ? a₂ cos θ and a₁ cos θ + a₂ sin θ could be a asymmetric beamsplitter’s two output fields. We show that the two transformations are concisely expressed in the parameterized coherent-entangled state representation as a projective operator in integration form.     

End modes in arrays of modulated Su–Schrieffer–Heeger chains

In this article, an extended and modulated version of the classic Su–Schrieffer–Heeger model is analysed. The nature of the end modes and the effect of cyclic modulation of the hopping parameters are studied in detail. The analysis is extended to the case of an array of linear chains described by the Su–Schrieffer–Heeger model, where the robustness of the end states for a large range of coupling strengths between the chains is found.     

The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

In this paper, the famous Klein–Gordon–Zakharov (KGZ) equations are first generalized, and the new special types of KGZ equations with the positive fractional power terms (gKGZE) are presented. In order to derive exact solutions of the new special gKGZE, subsidiary higher-order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aid of the sub-ODE, exact solutions of four special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal travelling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.     

A Shannon–Tsallis transformation

Via a first-order linear differential equation, we determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon’s or Tsallis’ entropies in the concomitant variational problem. It is shown that the two variations lead to equivalent solutions that have different appearances but contain the same information. These solutions are linked by our transformation. However, the so-called collision entropy (Tsallis’ one with q=2$q=2$) does not have a Shannon counterpart.     

The Fresnel—Weyl complementary transformation

Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation(for(a 1 a 2)/√ 2) and the Weyl transformation(for(a 1 + a 2)/√ 2).Physically,(a 1 a 2)/√ 2 and(a 1 + a 2)/√ 2 could be a symmetric beamsplitter’s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.     

The influence of microstructure on the martensitic transformation in Cu–Zn–Al melt-spun ribbons

The martensitic transformation was investigated in a set of twin roller melt-spun Cu–Zn–Al shape memory alloys, solidified at tangential wheel speeds between 20 and 40 m/s. The resulting microstructures were analyzed using X-ray diffraction, optical and transmission electron microscopy techniques. The characteristic martensitic transformation temperature, M _S, was determined for each condition by conventional resistometric methods. The ribbons are homogeneous in shape and for each quenching rate they exhibit a quite uniform M _S temperature. By proper thermal treatments, the different factors affecting M _S could be separately examined and from temperature measurements, the contribution of L2₁ antiphase boundaries evaluated. A calculation of this contribution using pair interchange energies is in good agreement with the experimental results.     

Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su–Schrieffer–Heeger(SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss–Bonnet theorem on the topologic...     

Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array

Floquet topological insulators(FTIs) have been used to study the topological features of a dynamic quantum system within the band structure. However, it is difficult to directly observe the dynamic modulation of band structures in FTIs. Here, we implement the dynamic Su–Schrieffer–Heeger model in periodically curved waveguides to explore new behaviors in FTIs using light field evolutions. Changing the driving frequency produces near-field evolutions of light in the high-frequency curved waveguide array that are equivalent to the behaviors in straight arrays. Furthermore, at modest driving frequencies,the field evolutions in the system show boundary propagation, which are related to topological edge modes. Finally, we believe curved waveguides enable profound possibilities for the further development of Floquet engineering in periodically driven systems, which ranges from condensed matter physics to photonics.     

The investigation of solid–solid phase transformation at CuAlNi alloy using molecular dynamics simulation

In this study the thermodynamic and structural properties of a CuAlNi model alloy (3A) system were investigated using a molecular dynamics (MD) simulation method. The interactions between atoms were modelled by the Sutton-Chen embedded atom method (SCEAM) based on many-body interactions. It was observed that at the end of thermal process the thermo-elastic phase transformation occurred in the model alloy system. In order to analyse the structures obtained from MD simulation, techniques such as thermodynamic parameters and radial distribution function (RDF) were used. The local atomic order in the model alloy was analysed using Honeycutt–Andersen (HA) method.     

Auto-Bäcklund transformation and exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order

In this Letter, based on the idea of homogeneous balance (HB) method and with help of Mathematica, we obtain a new auto-Bäcklund transformation for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Then based on the Bäcklund transformation, some solutions for these two equations are derived.     

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.