1993年, 第19卷, 第2期　
刊出日期：1993-03-15

  

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  The Staggered Magnetization of the Square Lattice Frustrated Heisenberg Model

  Shi-Min CUI

  理论物理通讯. 1993, 19(2): 129-138.

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  Spin-wave expansion is used to evaluate the staggered magnetization of frustrated antiferromagnetic (AF) Heisenberg model with next-nearest-neighbor exchange couplings on a square lattice to the order O(1/S) at zero temperature. It is shown that the O(1/S) order correction increases the staggered magnetization and its presence invalidates the conventional spin- wave conclusions at large frustrations. We apply the mean-field approximation to deal with the quartic terms in the Hamiltonian of the Holstein-Primakoff transformation. A phaqe diagtam is obtained, suggesting that the NCel order is not destroyed for S≥1 at any frustration, while for S = 1/2 there may exist a disordered phase for strong frustrations.
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  Perturbat ion Approach for the Localization Transition in the Dissipative Two-State System

  Guang-Ming ZHANG, Hong CHEN, Xiang WU

  理论物理通讯. 1993, 19(2): 139-144.

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  Analysis of a dissipative two-state system at zero temperature shows that the model Hamiltonian may be exactly reduced to a modified quantum sine-Gordon model, which describes the effective interactions between the low-frequency phonons under coupling with a tunneling system. Directly considering the infrared divergence encountered in the conventional perturbation treatment, we have developed a new perturbation approach for the effective Hamiltonian, and derived the exact critical conditions for the localization transition. In the critical regime, a gap will be opened near zero momentum in the elementary excitation spectrum of the low-frequency phonons, and the corresponding ground state wave function is found to be a pairing quasi-particle state, analogous to the BCS superconducting state.
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  Numerical Solution of the spin-3/2 Heisenberg Antiferromagnetic Chains Using a Projector Method

  Gang SUN, Fu-Cho PU

  理论物理通讯. 1993, 19(2): 145-150.

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  An efficient projector method is used to calculate the energies of the ground state and the first excited state, and hence the energy gap between them, of the spin-3/2 Heisenberg antiferromagnetic chains with linear sizes up to N = 32. For the chains up to N = 8 the exact results are obtained, and for longer chains up to N = 32 they are estimated by imposing on Monte Carlo technique. It is found that the size dependence of the ground state energy per site has the form of [eo(N) - eo] ～ 1/N², and the value of the ground state energy per site as N→∞ is eo = -2.8248. Our results show that the energy gap trends to zero as N→∞, which is consistent with the rigorous proof.
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  Dark and Bright Solitons of Extraordinary Waves in Ferromagnetic Systems

  Ying WU

  理论物理通讯. 1993, 19(2): 151-156.

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  It is shown that the slowly varying amplitudes of both high and low frequency extraordinary waves propagating perpendicular to the dc magnetic field in ferromagnetic systems are described by the nonlinear SchrEdinger equation. The extraordinary waves are modulationally stable (unstable) and may evolve as dark (bright) solitons as the frequency ω satisfies ω₀ < ω < ω_b or ω > ω₁(0 < ω < ω₀ or ω_a ≤ ω < ω₁), where ω_a, ω_b, ω₀ and w₁ are given in the text.
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  Scaling Exponents and Power Spectrum of Self-Organized Criticality

  Yu SHI, Chang-De GONG

  理论物理通讯. 1993, 19(2): 157-162.

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  A directed sandpile automaton is simulated on a triangular lattice. Water droplets on a window pane are argued to be in the same class of universality hence also in a self-organized critical state. Various scaling exponents are obtained. In agreement with experimental results, the power spectrum is shown to be f^-2-like instead of f^-1-like.
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  From Continuous to First Order Phase Transition in a Generalized XY Model

  Tian WANG, Tian-Lun CHEN

  理论物理通讯. 1993, 19(2): 163-168.

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  A generalized XY model with interaction V(θ) = 2 J{1 - [cos² (θ/2)]^p2} is studied by Monte Carlo renormalization group method on two-dimensional random triangle lattice. For p = √2, a line of fixed points has been found. It characterizes that there is a Kosterlitz-Thouless phase transition. For p = 2, a first order phase transition has been found. Both of them show the relationship between the nature of phase transition and the class of interactions.
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  The q-Deformed SU(2) Quantum Ferromagnetic Model

  Zhong-Yi LU, Hong YAN

  理论物理通讯. 1993, 19(2): 169-178.

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  A q-deformed SU(2) Heisen berg (3-dimensional) spin model is set up, and the q-deformed spin-wave solution is obtained through the q-analogous Holstein-Primakoff transformation. The result is given for small γ = In q, which is the quantity characterizing the nonlinearity of the Hamiltonian. A mean-field treatment is arranged to preserve (at least some of) the nonlinearity, and the ordinary ferromagnet ground state is shown as the exact ground state of the new system. Interesting results are obtained for this nonlinear model:(i) There is an energy gap between the ground state and the first excited one, thus the ground state is stable under small perturbation of the background; (ii) the specific heat per volume is modified by a small term proportional to the (1/2)-th power of temperature and the square of γ, which is qualitatively different from the conventional model, and (iii) the magnetization M (T) is modified by a factor that depends on γ.
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  A New Hopf Algebra and the Universal R-Matrix Associated with It

  Mo-Lin GE, Xu-Feng LIU

  理论物理通讯. 1993, 19(2): 179-184.

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  We present a new Hopf algebra and following Drinfeld's quantum double construction, we obtain an explicit formula for the universal R-matrix associated with it.
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  On GCT-Invariant Operator Ordering Rule

  De-Hai BAO, Zhong-Yuan ZHU

  理论物理通讯. 1993, 19(2): 185-190.

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  With an observation that the general coordinate transformation (GCT) invariant operator ordering rule proposed by DeWitt is valid only for some cases, a careful classification for classical observables that can be related through the well-defined GCT is presented and a generalized GCT-invariant ordering rule is derived.
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  Generalized Quasi-Exactly-Solvable Quanta1 Problems, the Represent at ions and Differential Realization of General Deformation of su(2)

  Chang-Pu SUN, Wei LI

  理论物理通讯. 1993, 19(2): 191-198.

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  This paper is devoted to building the represen tation theory of the general deformation for su(2) and then using it to generalize the quasi-exactly-solvable quan tal (QESQ) problems. For the finite dimensional and infinite dimensional representations, two classes of generalized QESQ models are respectively constructed in terms of the differential realization of the general deformation of su(2). When the deformation is the q-deformation in the quantum group theory, the QESQ model is discussed in detail by associating it with the nonlinear precession of high spins in an external field.
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  Analysis of Collective Flow in High Energy Heavy-Ion Collisions in the Relativistic VUU Approach

  Hong-Bo ZHOU, Zhu-Xia LI, Yi-Zhong ZHUO

  理论物理通讯. 1993, 19(2): 199-204.

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  We have calculated the collective flow for Ar+KCl collisions of 1200 MeV/A by using the relativistic Vlasov-Uehling- Uhlenbeck (VUU) equation based on the QHD-I model of Walecka. The tensitivity of flow characterized by C(ψ)a nd (P_x(Y))to mean field and in-medium NN scattering cross section is studied. It is found that the azimuthal correlation function C(ψ) is reduced dramatically after inserting the collision term and then varies very slowly between NN cross sections from σ = 10 mb to 55 mb and reaches the minimum at σ = 35 mb, while the in-plane mean transverse momentum (P_x(Y))in creases slowly all the way from σ = 0 mb to 55 mb. The collective flow is very sensitive to the momentum dependence (indicated by the effective mass m⁰) of the mean field and less sensitive to the compression modulus K and the cross sections from σ = 10 mb to 55 mb. The numerical results were compared with the experimental data, and we found that the agreement for both (P_x(Y)) and C(ψ) can be reached with the same set of mean field parameters as well as the appropriate NN cross section in collision terms.
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  Enhancement of the K⁺/π⁺ Ratio in High-Energy Proton-Nucleus and Nucleus-Nucleus Collisions due to the Final State Interactions

  Bo LIU, Huan-Ching CHIANG

  理论物理通讯. 1993, 19(2): 205-212.

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  The pion-meson secondary collisions with surrounding nucleons in the nucleus can influence the K⁺/π⁺ ratio. We calculate this effect in proton-nucleus and nucleus-nucleus collisions by the Glauber model and find that the final state interactions are important.
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  An Off-Shell qq Potential and Its Effect on the Meson Spectrum

  Yu-Bing DONG, Jun-Chen SU, Shi-Shu WU

  理论物理通讯. 1993, 19(2): 213-218.

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  An off-shell qq potential is derived from the effective interaction Harniltonian which appears in the relativistic Pauli-Schrödinger equation for quark-antiquark bound states. This potential gives considerable theoretical improvements on meson spectra.
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  Quark-Meson Bag Model and Hadron Structure

  Liang-Gang LIU

  理论物理通讯. 1993, 19(2): 219-224.

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  Based on the assumption that quarks (e.g. up, down quarks) couple with σ, ω and π mesons directly, a quark-meson bag model is-proposed. By adjusting the quark effective mass and quark-meson coupling constants, the nucleon, Δ baryon masses and some observables of proton are calculated.
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  Variational Study of 3-Dimensional SU(3) Lattice Gauge Theory with Independent Plaquette Trial Action

  Di GONG, Jin-Ming LIU

  理论物理通讯. 1993, 19(2): 225-230.

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  The phase structure of 3-dimensional SU(3) lattice gauge theory is studied by using the variational method wit11 an independent plaquette trial action. The mean plaquette internal cncrgy E_p～β curve is smooth, which shows only one confining phase, and is better than that given by the independent link trial action.
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  Chaotic Behavior of One-Dimensional Nonlinear Schrodinger Equations Involving High Order Saturable Nonlinear Terms

  Cang-Tao ZHOU, X.T. HE

  理论物理通讯. 1993, 19(2): 231-242.

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  The non-integrable behavior in one-dimensional generalized nonlinear Schr6dinger equations involving high order saturable nonlinearities, which govern the dynamic behavior in a class of physical systems, is investigated numerically. The numerical results illustrate that the high order saturable nonlinearities would lead to chaos, where the irregular homoclinic orbit (HMO) crossings have been observed in phase space. On the other hand, we show that the periodic solutions and solitary waves may exist in such non-integrable continuum Hamiltonian dynamic systems.
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  The Groundstate of 2-Dimensional Infinite-U Hubbard Model with a Single Hole

  Zhi SONG, Zhen-Qing YANG, Guo-Zhu HE

  理论物理通讯. 1993, 19(2): 243-246.

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  The groundstate energies of 1 - and 2-D infinite-U Hubbard models with a single hole are obtained by a simple method. It is found that the groundstates for an arbitrary finite system are multiple degenerate states with S_z = S, S - 1, …, -S (S = (N - 1)/2, N = even is the number of sites). Based on these results, it is shown that the hole and the spin-ffip(s) can not form a bound state, then it provides an alternate proof of Nagaoka's theorem.
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  Deforming the Travelling Wave Solutions of the KdV Equation to Those of the Generalized Fifth Order KdV Equation

  Sen-Yue LOU, De-Fang CHEN

  理论物理通讯. 1993, 19(2): 247-252.

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  Using some limiting procedures, the solutions of the fifth order KdV equation u_t + (μu²+ υu_xx + αuu_xx + βu_x² + γu³ + δu_xxxx)_x = 0 would degenerate into the solutions of a simple equation, say KdV equation. In this letter, we analyze the possibility of the inverse procedure of the limiting process mentioned above for the travelling wave solutions. The results show that the procedure for deforming a travelling wave solution of the KdV equation to that of the generalized fifth order KdV equation can be accomplished by some pure algebraic tricks. Moreover, this inverse procedure is not unique in general.
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  Quark Model for Nuclear Force

  Ren-Chang HOU, Xi-Jun QIU, Xiao-Ming XU

  理论物理通讯. 1993, 19(2): 253-256.

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  Relativistically the corrected transition potential of quark to quark-quark-antiquark is derived. With the input of the quark wave function and the quark-gluon coupling constant determined in a chird quark soliton model, this transition potential is used to obtain the deuteron binding energy in the resonating group method.