Matone's Relation ofN =2 Super Yang-Mills and Spectrum of Toda Chain

InN=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation <
Trφ²>. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.     

N=2超对称量子力学的新实现和形状不变性

构造新的超荷和定义权重函数,并研究了N=2一维超对称量子力学.在新的实现中讨论了若干实例.     

(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Modulation of Schottky barrier in XSi2N4/graphene (X=Mo and W) heterojunctions by biaxial strain

Reducing the Schottky barrier height (SBH) and even achieving the transition from Schottky contacts to Ohmic contacts are key challenges of achieving high energy efficiency and high-performance power devices. In this paper, the modulation effects of biaxial strain on the electronic properties and Schottky barrier of MoSi₂N₄ (MSN)/graphene and WSi₂N₄ (WSN)/graphene heterojunctions are examined by using first principles calculations. After the construction of heterojunctions, the electronic structures of MSN, WSN, and graphene are well preserved. Herein, we show that by applying suitable external strain to a heterojunction stacked by MSN or WSN — an emerging two-dimensional (2D) semiconductor family with excellent mechanical properties — and graphene, the heterojunction can be transformed from Schottky p-type contacts into n-type contacts, even highly efficient Ohmic contacts, making it of critical importance to unleash the tremendous potentials of graphene-based van der Waals (vdW) heterojunctions. Not only are these findings invaluable for designing high-performance graphene-based electronic devices, but also they provide an effective route to realizing dynamic switching either between n-type and p-type Schottky contacts, or between Schottky contacts and Ohmic contacts.