共查询到20条相似文献,搜索用时 31 毫秒
1.
《Nuclear Physics B》1995,448(3):429-456
Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite spin chain systems with integrable boundary conditions. We derive these equations using the properties of the vertex operators and the boundary vacuum state, or alternatively through corner transfer matrix arguments for the eight-vertex model with a boundary. The spontaneous boundary magnetization is found by solving such difference equations. The boundary S-matrix is also proposed and compared, in the sine-Gordon limit, with Ghoshal-Zamolodchikov's result. The axioms satisfied by the form factors in the boundary theory are formulated. 相似文献
2.
S.C. Lim 《Annals of Physics》2009,324(8):1676-1964
We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a4 when a→0+ and decays exponentially when a→∞. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case. 相似文献
3.
《Nuclear Physics B》2001,594(3):535-606
We study a single particle diffusing on a triangular lattice and interacting with a heat bath, using boundary conformal field theory (CFT) and exact integrability techniques. We derive a correspondence between the phase diagram of this problem and that recently obtained for the 2-dimensional 3-state Potts model with a boundary. Exact results are obtained on phases with intermediate mobilities. These correspond to nontrivial boundary states in a conformal field theory with 2 free bosons which we explicitly construct for the first time. These conformally invariant boundary conditions are not simply products of Dirichlet and Neumann ones and unlike those trivial boundary conditions, are not invariant under a Heisenberg algebra. 相似文献
4.
We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Lüscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory. 相似文献
5.
We study medium modifications of the dilepton e + e ? and μ+μ? mass spectra in coherent photo-and electroproduction of ρ0(1S)-and ρ′(2S)-meson resonances on nuclear targets. The analysis is performed within the coupled ρ0(1S), ρ′(2S), ... channel formalism, where nuclear modifications derive from off-diagonal rescatterings. We find that the effect of off-diagonal rescatterings on the shape of the dilepton-mass spectrum in the ρ0(1S)-meson mass region is only marginal, but it is very important in the ρ′(2S) mass region. The main off-diagonal contribution in the ρ′(2S) mass region comes from the sequential mechanism γ* → ρ0(1S) → ρ′(2S), which dominates ρ′(2S) production for heavy nuclei. Our results also show that, in the ρ′(2S) mass region, there is a considerable interference of the Breit-Wigner tail of the amplitude for the decay ρ0(1S) to e + e ? and μ+μ? with the amplitude for the decay of ρ′(2S) to e + e ? and μ+μ?. 相似文献
6.
《Nuclear Physics B》2005,711(3):565-603
We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S. 相似文献
7.
It was proposed about a decade ago [M.G.E. da Luz, A.S. Lupu-Sax, E.J. Heller, Phys. Rev. E 56 (1997) 2496] a simple approach for obtaining scattering states for arbitrary disconnected open or closed boundaries C, with different boundary conditions. Since then, the so called boundary wall method has been successfully used to solve different open boundary problems. However, its applicability to closed shapes has not been fully explored. In this contribution we present a complete account of how to use the boundary wall to the case of billiard systems. We review the general ideas and particularize them to single connected closed shapes, assuming Dirichlet boundary conditions for the C’s. We discuss the mathematical aspects that lead to both the inside and outside solutions. We also present a different way to calculate the exterior scattering S matrix. From it, we revisit the important inside-outside duality for billiards. Finally, we give some numerical examples, illustrating the efficiency and flexibility of the method to treat this type of problem. 相似文献
8.
《Nuclear Physics B》1999,542(3):659-693
We construct new non-diagonal solutions to the boundary Yang-Baxter equation corresponding to a two-dimensional field theory with Uq(a2(1)) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a2(1) affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions. 相似文献
9.
10.
This paper deals with the ion emission of a two-phase system composed of a copper single crystal matrix in which small precipitates of Al2O3 or BeO oxide of a few hundreds Å in diameter (from 60 to 470 Å) are included. It is observed that ions originate from three regions of the sample: region I. copper matrix: Cu+, Cu+2, Cu+3,…; region II. precipitates: Al+, Al+2, AlO+ Al2O+, …; respectively Be+, Be+2, BeO+ Be2O+,…; region III, matrix-precipitate interface: Cu+, CuAl+ or CuBe+,…. The presence of CuAl+ or CuBe+ ions and the enhancement of Cu+ emission at the periphery of precipitates in region III, makes the principle of the linear superposition of mass spectra of the two phases invalid. The interpretation of the results is based upon a simple model of sputtering which involves a coupling between the sputtering of precipitates and matrix. This model shows that, under steady state conditions, the surface density of precipitates is roughly proportional to the ratio S/Sp of the sputtering yields of the matrix and precipitates. We have taken advantage of the dependence of S on the crystal orientation of the sample with respect to the bombarding direction, to change the surface density of precipitates. Any change in S is followed by a time evolution of ion intensities originating from regions H and III. The average time of evolution allows one to characterize the size of precipitates. The sputtering process of a two-phase system (formation of cones) is discussed together with the ionization process. 相似文献
11.
《Nuclear Physics B》2002,636(3):497-513
In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space–time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular S-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter. 相似文献
12.
Rajan Murgan 《Czechoslovak Journal of Physics》2006,56(10-11):1237-1242
We review recent results on the Bethe ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters α?, α+, β?, β+ are nonzero. A generalization of the BaxterT-Q equation that involves more than one independentQ is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary. 相似文献
13.
We develop a new type of derivative matrix for pseudospectral methods. The norm of these matrices grows at the optimal rate O(N2) for N-by-N matrices, in contrast to standard pseudospectral constructions that result in O(N4) growth of the norm. The smaller norm has a big advantage when using the derivative matrix for solving time dependent problems such as wave propagation. The construction is based on representing the derivative operator as an integral kernel, and does not rely on the interpolating polynomials. In particular, we construct second derivative matrices that incorporate Dirichlet or Neumann boundary conditions on an interval and on the disk, but the method can be used to construct a wide variety of commonly used operators for solving PDEs and integral equations. The construction can be used with any quadrature, including traditional Gauss–Legendre quadratures, but we have found that by using quadratures based on prolate spheroidal wave functions, we can achieve a near optimal sampling rate close to two points per wavelength, even for non-periodic problems. We provide numerical results for the new construction and demonstrate that the construction achieves similar or better accuracy than traditional pseudospectral derivative matrices, while resulting in a norm that is orders of magnitude smaller than the standard construction. To demonstrate the advantage of the new construction, we apply the method for solving the wave equation in constant and discontinuous media and for solving PDEs on the unit disk. We also present two compression algorithms for applying the derivative matrices in O(N log N) operations. 相似文献
14.
《Nuclear Physics B》1999,558(3):637-667
We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or A1(1) model, Izergin-Korepin or A2(2) model, sl(2|1) model and the osp(2|1) model. We find that there is a general solution for A1(10) and sl(2|1) models. In both models it is a complete K-matrix with three free parameters. For the A2(2) and os(2|1) models we find three general solutions, being two complete reflection K-matrices solutions and one incomplete reflection K-matrix solution with some null entries. In both models these solutions have two free parameters. Integrable spin-1 Hamiltonians with general boundary interactions are also presented. Several reduced solutions from these general solutions are presented in the appendices. 相似文献
15.
The energies of the bound 0+ states of the α-particle are calculated on the basis of four body integral equations with separable 1S0 and 3S1 pair interactions. We find the ground state at z1 = ?45.73 MeV and an excited o+ level is found to be ?11.69 MeV. 相似文献
16.
《Physics letters. [Part B]》1999,456(1):60-67
It has been proposed recently that the scale of quantum gravity (“the string scale”) can be MS∼few TeV with n≥2 extra dimensions of size R≲mm so that, at distances greater than R, Newtonian gravity with MPl∼1018 GeV is reproduced if MPl2∼RnMSn+2. Exchange of virtual gravitons in this theory generates higher-dimensional operators involving SM fields, suppressed by powers of MS. We discuss constraints on this scenario from the contribution of these operators to the processes e+e−→W+W−, ZZ, γγ. We find that LEP2 can place a limit MS≈1 TeV from e+e−→W+W−, ZZ, γγ. 相似文献
17.
Huai-Yu Wang 《Physics letters. A》2009,373(37):3374-3380
We present a comprehensive theory that reduces the total power of products of spin operators. This theory improves the previous one [P.J. Jensen, F. Aguilera-Granja, Phys. Lett. A 269 (2000) 158] in two aspects. One is that for the set of spin operators S+, S−, Sz, a new method is suggested where the expansion coefficients in the reduction formula can be solved from linear equations. This new method is of direct physical meaning and is easier to handle. The other is that we show a method to reduce the products of another set of spin operators Sx, Sy, Sz. For this set of operators, the use of permutation regulation of x→y, y→z and z→x can save much time in obtaining some reduction formula. The present comprehensive theory enables one to deal more easily with the decoupling problems in Green' function theory where the set of either S+, S−, Sz or Sx, Sy, Sz operators is used. 相似文献
18.
We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called ST-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the PQRS-form, also gives a natural scheme to design generalized low and high pass quantum filters. 相似文献
19.
《Nuclear Physics B》1995,441(3):437-470
The XXZ spin chain with a boundary magnetic field h is considered, using the vertex operator approach to diagonalize the hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are three distinct regions when h ⩾ 0, in which the structure of the vacuum states is different. Excited states are given by the action of vertex operators on the vacuum states. We derive the boundary S-matrix and present an integral formula for the correlation functions. The boundary magnetization exhibits boundary hysteresis. We also discuss the rational limit, the XXX model. 相似文献
20.
T. Sh. Navasardyan A. A. Saharian 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2017,52(4):348-354
The Casimir forces, acting on the parallel plates in models with the compact subspace are investigated for the case of a scalar field. The field obeys the Robin boundary conditions on the plates. Depending on the values of the coefficients in the boundary conditions, the forces can be either attractive or repulsive. In models with a homogeneous compact subspace, they are the same for both the plates. In special cases of the Dirichlet and Neumann boundary conditions, the Casimir forces are attractive. Proceeding from general results, two particular cases with the subspaces S1 and S2 are considered. 相似文献