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In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator on the rational noncommutative orbifold T2/Z4. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.

The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.

From the ? symmetric action of IIB string in AdS2?S2 background given by Zhou, we derive the equations of motion. By using the twisted dual transformation which was introduced by Hou, we construct the flat currents, conserving non-local charge with one free parameter, for the superstring in AdS2?S2.

We study the quantum standard teleportation based on the generic measurement bases. It is shown that the quantum standard teleportation does not depend on the explicit expression of the measurement bases. We have given the correspondence relation between the measurement performed by Alice and the unitary transformation performed by Bob. We also prove that the single particle unknown states and the two-particle unknown cat-like states can be exactly transmitted by means of the generic measurement bases and the correspondence unitary transformations.

In this paper, we recast the matter part of the open superstring star in the present of a constant B field. By using a different coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables. Fortunately we find it does not depend on the value of the B field.

In this paper we generalize the standard teleportation to the conclusive teleportation case which can teleport an arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that only if the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state be perfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle states and for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typical examples are given so that one can see how our method works.

The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess–Zumino–Witten-like term.

By making use of the theoretical framework presented by Bostroem (K. J. Bostroem, LANL quant-ph/0009052), we generalize the standard quantum information theory of block messages with fixed block length to the variable one. We show that the states belonging to a sufficiently large Hilbert space are the highly distinguishable states. We also consider the collection states (product states of more than one qubit state) and seek a ``pretty good measurement"(PGM) with measurement vectors to improve the mutual information. The average mutual information over random block-message ensembles with variable block length n is discussed in detail.

By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge group space we get WZW effective Lagrangian on high dimensional non-commutative space.Especially consistent anomalies derived from this WZW effective action in non-commutative four-dimensional space coincides with those by L.Bonora etc., Comment: 9 pages, latex, no figures

In this paper, we detail the theoretical ideas which are used to explain the mechanism of the laser controlling the geometric quantum gates introduced in the work by Ekert et al. (Ekert A, Ericsson M, Hayden P, Inanori H, Jones J A, Oi D K L and Vedral V 2000 J. Mod. Opt. 47 2501). We have introduced a two-level Hamiltonian system and directed to solve this system and then obtained the probability distribution of this two-level system. We also show the relationships between the external laser fields and the transition of the qubit in the two-qubit controlled-phase gate and how the transition of the qubit depends on the external laser fields and the states of the controlled qubit.

We propose a rational quantum deformed nonlocal currents in the homogenous space $SU(2)_k/U(1)$, and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level $k=c$ is obtained. In the classical limit $\hbar \to 0$, the quantum nonlocal currents become $SU(2)_k$ parafermion, and the realization of Yangian double becomes the parafermion realization of $SU(2)_k$ current algebra., Latex, 9 pages

In this paper, we obtain the eigenstates and the eigenvalues of the Hamiltonians of the trigonometric SU(N) Gaudin model based on the quasi-classical limit of the trigonometric SU(N) chain with the periodic boundary condition. By using the quantum inverse scattering method, we also obtain the eigenvalues of the generating function of the trigonometric SU(N) Gaudin model.

The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain. After the quantum determinant being well defined, the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Gaudin model are given. These results can be generalized to any number of constituting spins (SU(N)).

We derive a free boson representation of the Yangian double DY(slN) 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.

The eigenvalue of the transfer matrix is obtained for the extended Essler-Korepin-Schoutens model with open boundary conditions. The energy of the system and the Bethe equations of the model are given also.

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.

The Lax pair and corresponding boundary K-matrices for the XXC model are derived. The time-independent transfer matrix with the spectral parameter is constructed, which means the system to be Lax integrable. Our K-matrices include the result used by Arnaudon and Maassarani (D. Arnaudon and Z. Maassarani, lapth-695/98, laval-phy-22/98) as a special case.

We propose a dynamical elliptic algebra which is based on the relations RLL = LLR*, where R and R* are the dynamical R-matrices of -type face model with the elliptic module shifted by the center of algebra. nom the high-rank Gauss decomposition,h we obtain the Drinfeld currents of dynarnical elliptic algebra .

By using algebraic Bethe ansatz method, we give the Hamitonian of the spin-1 XXX chain associated with $sl_2$ with two boundary impurities., 8 pages, latex, no figures, to be appeared in Commun. Theor. Phys

By using the fusion method, we give the spin-1 XXX chain associated with sl2 with two arbitrary spin boundary impurities. Then the exact diagonalized Hamiltonian of this model was obtained by the means of Bethe ansatz method.

As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ħ, we get the commutation relation and the bosonization of quantum ħ-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type I and type II intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of and actually give the exact scattering matrix of the restricted sine-Gordon model.

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also study the boundary bound state for this case.

By compactifying the four-dimensional Euclidean space into S2 × S2 manifold and introducing two topological relevant Wess–Zumino terms to Hn ≡ SL(n,c)/SU(n) nonlinear sigma model, we construct a Lagrangian form for SU(n) self-dual Yang–Mills field, from which the self-dual equations follow as the Euler–Lagrange equations.

A free field representation for the left-right asymmetric conformal Toda theory based on simply-laced even-rank Lie algebras is given. It is shown that the classical chiral exchange algebra for such theories can be reconstructed from free chiral bosons via Drinfeld-Sokolov linear systems, and is a bit more complicated than that of the standard Toda due to some additional -function terms and extra degrees of freedom.

We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N) Gaudin model based on the quasi-classical limit of the SU(N) chain under the periodic boundary condition. Using the quantum inverse scattering method, we also obtain the eigenvalues of the generation function of the rational SU(N) Gaudin model.

The Perk-Schultz model with SUq(m|n) spin boundary impurities is constructed by dressing the c-number reflecting K-matrix with the local L-matrix which acts non-trivially on an impurity Hilbert space. The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method (m≠n). When m = 1,n = 2, our results come back to that of supersymmetric t-J model with SUq(1|2) spin boundary impurities.

For the Zn-symmetric statistical model the Yang-Baxter equation and the equations for the operator representations is reduced to explicit spectroparameter-independent forms, and the quantum algebra for the representations is obtained. Moreover, we present some elliptic representations of braid group, which include a new trigonometric representation as degenerated case.