We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.
Chinese ancient sage Laozi said that everything comes from'nothing'.Einstein believes the principle of nature is simple.Quantum physics proves that the world is discrete.And computer science takes continuous systems as discrete ones.This report is devoted to deriving a number of discrete models,including well-known integrable systems such as the KdV,KP,Toda,BKP,CKP,and special Viallet equations,from'nothing'via simple principles.It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra,model-independent nonlinear superpositions of a trivial integrable system(Riccati equation),index homogeneous decompositions of the simplest geometric theorem(the angle bisector theorem),as well as the Möbious transformation invariants.
In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances.
We study the optical field's quadrature excitation state X m |0 , where X = (a+a+)/ √2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.
In order to describe the characterization of resistive drift-wave fluctuation in a tokamak plasma,a coupled inviscid two-dimensional Hasegawa–Wakatani model is investigated.Two groups of new analytic solutions with and without phase shift between the fluctuant density and the fluctuant potential are obtained by using the special function transformation method.It is demonstrated that the fluctuant potential shares similar spatio–temporal variations with the density.It is found from the solutions without phase shift that the effect of the diffusion and adiabaticity on the fluctuant density is quite complex,and that the fluctuation may be controlled through the adiabaticity and diffusion.By using the typical parameters in the quasi-adiabatic regime in the solutions with phase shift,it is shown that the density gradient becomes larger as the contours become dense toward the plasma edge and the contours have irregular structures,which reveal the nonuniform distribution in the tokamak edge.
The formal series symmetry approach(FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N= 1 supersymmetric Boiti–Leon–Manna–Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f(t). Some interesting special cases of symmetry algebras are presented, including a limit case f(t) = 1 related to the commutativity of higher order generalized symmetries.
