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We proposed a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled single-molecule magnets, $[\textrm{Mn}_4]_2$. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between the quantum computing bases and between the quantum computing bases and other excited states are evaluated and analyzed., Comment: 7 pages, 2 figures

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$., Comment: 8 pages, Latex file

The shift operators for XXX-Heisenberg chain are found. They are formed by local Yangian operators and the amplitutes of the eigenfunctions obeying Bethe ansatz for the Hamiltonian. The physical implication of the shift operators are also explained., Comment: 12 pages, Latex file

We show that there exists quantum group symmetry $ sl_{q}(2) $ in the fractional quantum Hall effect (FQHE) and this symmetry governs the degeneracy of ground-state level. Under the periodic boundary condition, the degeneracy of the ground state is related to the cyclic representation of SL_q(2). We also discuss the influence of impurity., Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. Submitted to Phys. Rev. B. To request a hard copy, write to Prof. Mo-lin Ge, Director of Nankai Institute of Mathematics. Do not send emails to this computer account

This is an introduction to the physical pictures of {\em Yangian} symmetry. All the discussions are based on the RTT relations which have been known to be related to the Hamiltonian formulations for quantum integrable systems. The explicit calculations of {\em Yangian} associated with $gl(2)$ are given through solving the RTT relations. It contains the Drinfeld's $Y(sl(2))$, $Y(sl(n))$ and Heisenberg type of Hopf algebras. Examples are emphasized to show the physical pictures, such as Hubbard model, Haldane-Shastry model, Long-range interaction models and Goryachev-Chaplygin(G-C) gyrostat. The example of the trigonometric extension of G-C gyrostat are also shown that leads to the non-commutative geometry naturally on the basis of the truncated $q$-affine algebra., Comment: 41 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. Invited talk presented at Second Pacific Physics Winter School. For hard copy, write to Prof. Mo-lin GE, Nankai Institute of Mathematics. Do not send emails to this computer account

An alternative approach to the Jaynes-Cummings model (JCM) with dissipation at a finite enviromental temperature is presented in terms of a new master equation under Born-Markovian approximations. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in the JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics., Comment: Preprint of Nankai Institute of Mathematics, CHINA. For hard copy, write to Prof. Mo-lin Ge, Director of Nankai Institute of Mathematics. Do not send emails to this computer account

In this paper, we study the supercurrent in a mesoscopic Josephson junction (MJJ) and its quantum statistical properties in the presence of nonclassical light fields. We investigate in detail the influence of external nonclassical light fields on current-voltage step structures of the MJJ. We also study in detail quantum statistical properties of the supercurrent when the external quantum electromagnetic fields are even and odd coherent-state light fields. It is shown that the supercurrent in the MJJ exhibits both squeezing effect and quantum coherences. It is demonstrated that the MJJ can feel the difference not only between classical light fields and nonclassical light fields but also between different nonclassical light fields., Comment: 21 papes, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin Ge, Director of Nankai Institute of Mathematics. Do not send emails to this computer account

We show that there is a kind of quantum group symmetry $ sl_{q}(2) $ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $ sl_{q}(2) $., Comment: 10 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Director of Nankai Institute of Mathematics. Do not send emails to this computer account

We investigate Wilczeck's mutual fractional statistical model at the field- theoretical level. The effective Hamiltonian for the particles is derived by the canonical procedure, whereas the commutators of the anyonic excitations are proved to obey the Zamolodchikov-Faddeev algebra. Cases leading to well known statistics as well as Laughlin's wave function are discussed., Comment: Preprint of Nankai Institute of Mathematics, China

The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and tunneling and localization are studied in detail. The broken symmetry condition and Langevin-like dissipative equation of motion are obtained. Some special dynamic features are considered., Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE. Do not send emails to this computer account

The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not only is the dynamics of the system periodic, but also its period is the same as that of the external potential. A model system in a periodic $\delta$-function potential is studied thoroughly., Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this computer account please

The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is shown to generate both models. We finally introduce the reflection algebra K(u) to the long range models., Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical Physics Division ), published in Physical Review E of 1995. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this account

Based on the RTT relation for a given rational $R$-matrix the {\em Yangian} and truncated {\em Yangian} are discussed. The former can be used to generate the long-range interaction models, whereas the latter can be related to the Goryachev-Chaplygin(GC) gyrostat. The trigonometric extension of the Goryachev-Chaplygin gyrostat has also been shown., Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Nankai Institute of Mathematics. Do not send emails to this computer account