Yangian Realization for Dirac Oscillator

We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operators for different energy levels for this system are obtained.     

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the "spin triplet" and the "spin singlet" that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.     

Yangian symmetries and integrability of the Dirac equation with spin symmetry

We show that a Yangian symmetry, namely, Y(su(2))$Y\left(su\left(2\right)\right)$, exists in the Dirac equation with spin symmetry when the potential term takes a Coulomb form. We construct the generators of Y(su(2))$Y\left(su\left(2\right)\right)$ explicitly and get the energy spectrum of this model from the representation theory for Y(su(2))$Y\left(su\left(2\right)\right)$. We also show that this model is integrable, from RTT relations.     

Traces of Intertwining Operators for the Yangian Double

The traces over infinite-dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special combinations of the intertwining operators, the traces are identified with form factors of local operators in the SU(2)-invariant Thirring model. This identification is based on the identities which are deformed analogs of the Gauss–Manin connection identities for the hyperelliptic curves.     

A Realization of Yangian and Its Applications in Addition of Angular Momenta

A realization of Yangian associated with SL(2) has been constructed. Using its shift operators, we discuss Clebsch-Gordan coefficients and other applications in addition of angular momenta.     

Free Field Representation of Level-k Yangian Double DY(sl2) k and deformation of Wakimoto Modules

A free field representation of level-k (0,–2) Yangian double DY(sl₂) _k and a corresponding deformation of Wakimoto modules are presented. We also realize two Types of vertex operators intertwining these modules.     

Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.     

Yangian symmetry in deformed WZNW models on squashed spheres

We introduce a deformation of the Wess-Zumino-Novikov-Witten model with three-dimensional squashed sphere target space. We show how with an appropriate choice of Wess-Zumino and boundary terms it is possible to construct an infinite family of conserved charges realizing an SU(2) Yangian. Finally we discuss the running of the squashing parameter under renormalization group flow.     

Dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed.     

Unitary Operator of su q (n)-Covariant Oscillator Algebra

The unitary operator of su _q (n)-covariant oscillator algebra is constructed and two types of q-coherent states are obtained explicitly.     

Common Shift Operators of {H,L2} for N-Dimensional Harmonic Oscillator

The common shift operators of {H, L²} for N-dimensional harmonic oscillator are established.     

Further Understanding of Hydrogen Atom: Yangian Approach and Physical Effect

By applying the representation theory of Y(sl(2)) to Hydrogen atom (HA) the correct spectrum are re-derived. This indicates the consistence between HA and the Yangian algebraic structure and guarantees that there is democracy between angular momentum L and Yangian current J in the sense of conserved currents. The physical effect of Yangian in HA has been predicted that preserves all the known results for HA, but gives rise to abnormal intensities in the spectrum lines near the free state.     

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.     

Universal R-matrix of the Super Yangian Double DY (gl(1|1))

Based on Drinfeld realization of super Yangian double DY (gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization L^±(u) of DY (gl(1|1)) is obtained. These two realizations of DY (gl(1|1)) are related by the supersymmetric extension of Ding-fienkel map.     

Another Free Boson Representation of Yangian Double DYħ(slN) with Arbitrary Level

We derive a free boson representation of the Yangian double DY_ħ(sl_N) with arbitrary level k by the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents cannot be obtained in the same way. From this point of view, the Yangian double with centre cannot be regarded as the degenerated case of the quantum affine algebra.     

Yangian代数在混合介子态的纠缠和衰变中的应用

Yangian代数是超出李代数更大的无穷维代数,是研究非线性量子完全可积系统的新对称特性的有力数学工具.基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性,本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(π~±,K~±,K~0和K~0)各自组成的三种混合介子态(π,K和K_i~0)衰变中的作用.将Y(su(3))代数的八个生成元(I~±,U~±,V~±,I~3和I~8)作为跃迁算子,作用在混合介子态上,研究其可能的衰变道,以及衰变前后纠缠度的变化.结果表明:1)在李代数范围内的生成元I~3和I~8作用下,三种混合介子态衰变后组成成分没有发生变化,其中混合介子态π在I~8作用下衰变前后纠缠无变化,其他衰变纠缠度发生了变化;2)在其他的六个(I~±,U~±和V~±)超出李代数的生成元的作用下,三种混合介子态衰变前后组成成分发生了变化,其中两个衰变后变成单态,纠缠度为零;两个衰变不存在;剩余两个衰变后纠缠度发生了变化,此外在带电(K)和中性(K_I~0)两类K型混合介子态的六种可能的衰变中,两种类型的末态的纠缠度两两相同;3)三种混合介子态之间可以通过I~±,U~±和V~±算子循环转化,具有明显的对称性.本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法,并且可以用此方法去预测可能的未知衰变粒子和解释己测得的衰变问题.     

Yangian symmetry in molecule {V6} and four-spin Heisenberg model

The symmetry operator Q = Y² is introduced to re-describe the Heisenberg spin triangles in the {V6} molecule, where Y stands for the Yangian operator which can be viewed as special form of Dzyaloshinsky–Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four -spins commutes with Q, which mean that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian H₄ for the model allows to take the total spin S = 1 by choosing some suitable exchange constants in H₄. In analogy to the molecule {V6} where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule “{V8}” model which is comprised of two parallelograms. Following the example of molecule {V15}, we give another theoretical molecule model regarding the four -spins system with total spin S = 1 and predict the local moments to be , respectively.     

Dynamically Induced Excitonic Instability in Pumped Dirac Materials

Driven and non-equilibrium quantum states of matter have attracted growing interest in both theoretical and experimental studies in condensed matter physics. Recent progress in realizing transient collective states in driven or pumped Dirac materials (DMs) is reviewed herein. In particular, the focus is on optically pumped DMs which are a promising platform for transient excitonic instabilities. Optical pumping combined with the linear (Dirac) dispersion of the electronic spectrum offers a knob for tuning the effective interaction between the photoexcited electrons and holes, and thus provides a way of reducing the critical coupling for excitonic instability. As a result, a transient excitonic condensate could be achieved in a pumped DM while it is not feasible in equilibrium. A unifying theoretical framework is provided for describing transient collective states in 2D and 3D DMs. The experimental signatures are described and numerical estimates of the size of the dynamically induced excitonic gaps and the values of the critical temperatures for several specific systems, are summarized. In addition, general guidelines for identifying promising material candidates are discussed. Finally, comments are provided regarding recent experimental efforts in realizing transient excitonic condensate in pumped DMs, and outstanding issues and possible future directions are outlined.     

The Construction of Dirac Wave Packets for a Fermionic Particle Non-Minimally Coupling with an External Magnetic Field

We shall proceed with the construction of normalizable Dirac wave packets for fermionic particles (neutrinos) with dynamics governed by a “modified” Dirac equation with a non-minimal coupling with an external magnetic field. We are not only interested on the analytic solutions of the “modified” Dirac wave equation but also on the construction of Dirac wave packets which can be used for describing the dynamics of some observable physical quantities which are relevant in the context of the quantum oscillation phenomena. To conclude, we discuss qualitatively the applicability of this formal construction in the treatment of chiral (and flavor) oscillations in the theoretical context of neutrino physics. PACS numbers: 02.30.Cj, 03.65.Pm