Chiral Potts model as a descendant of the six-vertex model

We observe that theN-state integrable chiral Potts model can be considered as a part of some new algebraic structure related to the six-vertex model. As a result, we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral Potts model transfer matrix.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

The representation of waist-to-waist transformation of Gaussian beams by the scaled fractional Fourier transform

The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed.     

Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 1999     

Validity of the transfer-matrix method for a two-dimensional electron waveguide

We solve the singularity problem of the transfer matrix method for a two-dimensional electron wave guide consisting of a sequence of cells. The method is reformulated in terms of intrinsic Bloch waves of a device cell. The resulting method is proved to be both stable and accurate. The transfer matrix is formulated without divergence problems in the open-mode approximation. The formula relating the N-cell transmission probability with that of one cell in the single-mode approximation takes exactly the same form as in the one-dimensional case.     

New Developments in the Eight Vertex Model

We demonstrate that the Q matrix introduced in Baxter's 1972 solution of the eight vertex model has some eigenvectors which are not eigenvectors of the spin reflection operator and conjecture a new functional equation for Q(v) which both contains the Bethe equation that gives the eigenvalues of the transfer matrix and computes the degeneracies of these eigenvalues.     

New Developments in the Eight Vertex Model II. Chains of Odd Length

We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity pointsη=mK/L with m odd the transfer matrix is known to satisfy the famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(υ) matrix is qualitatively different from the case of evenN and in particular they satisfy a previously unknown equation which is more general than what is often called ‘‘Bethe’s equation.’’ For the case of even m where no Q(υ) matrix is known we demonstrate that there are many states which are not obtained from the formalism of the SOS model but which do satisfy the TQ equation. The ground state for the particular case of η=2K/3 and N odd is investigated in detail.     

利用三粒子纠缠态建立量子隐形传态网络的探讨

利用W态纠缠源可以产生三纠缠粒子，用这些相互纠缠的粒子作为量子信道，再辅以经典信道传送Bell基联合测量信息和von Neumann测量信息，便可实现量子隐形传态网络.基于上述思想，研究了三纠缠粒子量子隐形传态网络的物理基础，得到了基于三粒子W 关键词： 量子通信 量子隐形传态 W态')" href="#">W态     

Extended nature of coupled optical interface modes in Thue-Morse dielectric superlattices

We investigate coupled optical interface modes in Thue-Morse (TM) dielectric superlattices composed of two kinds of materials with frequency-dependent dielectric functions. Four basic transfer matrices are derived in the dielectric continuum approximation. By a standard matrix operation method, the trace map of the global transfer matrix in this configuration is obtained. Under Born-von Kármán boundary conditions, the frequency spectra are calculated and their branching rules together with the quartet property are elucidated. It is further proved rigorously that nearly all eigenmodes in this framework have extended nature. The quartet of the eigenmodes is illuminated analytically. The common features and pronounced differences compared with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with other collective elementary excitations in TM structures are also revealed. Received 24 September 2002 / Received in final form 11 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: gjin@nju.edu.cn     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Continuously infinite commensurate-incommensurate phase transition of a two-dimensional competing Ising model

We consider the critical behavior of a two-dimensional competing axial Ising model including interactions up to third nearest neighbors in one direction. On the basis of a low-temperature analysis relating the transfer matrix of this model with the Hamiltonian of theS = 1/2XXZ chain, it is shown that the usual square root singularity dominating commensurate-incommensurate phase transitions of two-dimensional systems merges into a continuously infinite transition for certain relations among the coupling parameters. The conjectured equivalence between the maximum eigenstate of the transfer matrix associated with this model and the ground state of theXXZ chain is tested numerically for lattice widths up to 18 sites.     

A Note on the Bethe Ansatz Solution of the Supersymmetric t-J Model

The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain polynomials. We also show that the corresponding transfer matrix eigenvalues agree.     

Symmetry and transport of waves in one-dimensional disordered systems

The transfer matrix approach to transport in one-dimensional systems is reviewed in detail with emphasis on the role of symmetrized products. First, the concept of a transfer matrix is introduced, and then generalized through the introduction of symmetrized products. The resulting formalism is successively applied to the problem of averaging: resistance, density of states, conductance (i.e. transmission coefficient), phases of transmission and reflection, and frequency response. Finally the problem of 1/f noise in disordered systems is addressed in the language of symmetrized transfer matrices.     

Nondynamical calculation of polarization observables in the3H(d,n)4 He reaction below 1 MeV

The parametrization of cross-section, polarization, analysing powers, spin-correlation and polarization transfer observables in terms of (l, s, J) matrix elements is given for the³H(d, n)⁴He reaction at low energies. It is shown that a complete set of matrix elements can be obtained from these observables.     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Superexchange interaction enhancement of the quantum transport in a DNA-type molecule

We use the transfer matrix method and the Green function technique to theoretically study the quantum tunnelling through a DNA-type molecule. Ferromagnetic electrodes are used to produce the spin-polarized transmission probability and therefore the spin current. The distance-dependent crossover comes from the topological variation from the one-dimensional to the two-dimensional model transform as we switch on the interstrand coupling; a new base pair will present N-1 extrachannels for the charge and spin as N being the total base pairs. This will restrain the decay of the transmission and improve the stability of the quantum transport. The spin and charge transfer through the DNA-type molecule is consistent with the quantum tunneling barrier.     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Boundary critical behaviour of two-dimensional random Potts models

Using extensive Monte Carlo simulations, transfer matrix techniques and conformal invariance, ferromagnetic random q-state Potts models for are studied in the vicinity of the critical temperature. In particular the surface and bulk magnetization exponents and are found monotonically increasing with q. At the critical temperature, different moments (n) of the magnetization profiles are calculated which are all found to accurately follow predictions of conformal invariance. The critical correlation functions show multifractal behaviour, the decay exponents of the different moments both in the volume and at the surface, are n-dependent. Received 4 June 1999     

Finite-size scaling corrections for the eight-vertex model

Finite-size scaling corrections are calculated analytically for two of the maximal eigenvalues of the transfer matrix in the isotropic eight-vertex model. The valuec=1 for the conformal anomaly of the Virasoro algebra is confirmed.     

Temperature dependence of the stress transfer for thermal resistance polymer composites by X-ray diffraction

Temperature dependence of the stress transfer from the matrix resin to the incorporated fiber has been measured for poly(p-phenylene benzobisoxazole) (PBO) fiber/bismaleimide (BMI) resin composite by a novel X-ray diffraction method. At 120°C, stress transfer and tensile strength of the PBO/BMI composite are superior to that of the PBO/epoxy composite, due to the excellent thermal resistance and good mechanical property of BMI resins. The PBO/BMI composite possesses good adhesion and excellent mechanical properties at high temperature, which are suitable for thermal resistance applications.