A multispecies Calogero-Sutherland model

Motivated by the concept of ideal mutual statistics, we study a multispecies Calogero-Sutherland model in which the interaction parameters and masses satisfy some specific relations. The ground state is exactly solvable if those relations hold, both on a circle and on a line with a simple harmonic potential. In the latter case, the one-particle densities can be obtained using a generalization of the Thomas-Fermi method. We calculate the second virial coefficients in the high-temperature expansion for the pressure. We show that the low-energy excitations are the same as those of a Gaussian conformal field theory. Finally, we discuss similar relations between the statistics parameters and charges for a multispecies anyon model in a magnetic field.     

Correlation functions in the Calogero-Sutherland model with open boundaries

Calogero-Sutherland models of type BC_N are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions. Their asymptotic behaviour supports the predictions of (boundary) conformal field theory for the orthogonality catastrophy and Friedel oscillations. Received: 12 February 1998 / Accepted: 17 March 1998     

Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.     

三粒子Calogero-Sutherland模型的相干态

利用赝角动量算符方法求解三粒子CSM(Calogero-Sutherland Model)的类径向方程,给出本征态和相干态的解析表达式. 关键词： 三粒子Calogero-Sutherland模型 赝角动量算符方法 相干态     

Dynamic structure factor of the Calogero-Sutherland model

We evaluate the dynamic structure factor S(q, omega) of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small q, the structure factor differs from zero in a finite interval of frequencies of the width deltaomega proportional to q2/m. At the borders of this interval S(q, omega) exhibits power-law singularities with exponents depending on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the x-ray absorption spectra of metals.     

Dynamical correlation functions in the Calogero-Sutherland model

We compute the dynamical Green function and density-density correlation in the Calogero-Sutherland model for all integer values of the coupling constant. An interpretation of the intermediate states in terms of quasi-particles is found.     

The Calogero-Sutherland Model and Generalized Classical Polynomials

Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schr?dinger operators for Calogero-Sutherland-type quantum systems. For the generalized Hermite and Laguerre polynomials the multidimensional analogues of many classical results regarding generating functions, differentiation and integration formulas, recurrence relations and summation theorems are obtained. We use this and related theory to evaluate the global limit of the ground state density, obtaining in the Hermite case the Wigner semi-circle law, and to give an explicit solution for an initial value problem in the Hermite and Laguerre case. Received: 16 August 1996 / Accepted: 21 January 1997     

The Lee model with a symmetry and its renormalizability

The Lee model with a ‘symmetry’ condition m_o = m_N, where m_o is the bare V-particle mass, is investigated. The renormalization constant Z is always finite and lies between 1 and 0. No ghost state appears. The divergences in our model are not removable by renormalization procedures.     

Neuron model with conductance-resistance symmetry

This paper is to derive a mathematical model for neuron by imposing only a principle of symmetry that two modelers must obtain the same model when one models the conductances of ion channels and the other models the channels' resistances. Conductance-voltage characteristics for ion transport channels and protein gating channels are both derived. They are expressed as products of maximal conductances and opening probabilities for both types of channel. It gives an explanation to the role of spontaneous firing of individual channel pores and to the origin of leak current. The model has a better fit to a classical data than the Hodgkin-Huxley model does. It can also be reduced to a 2-dimensional model qualitatively similar to the FitzHugh-Nagumo equation and be expanded to a model of three ion channels capable of spike bursts.     

Spin-dependent extension of Calogero-Sutherland model through anyon-like representations of permutation operators

We consider a A_N−1 type of spin-dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard su(M) invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator P_ij, which pick up non-trivial phase factors along with interchanging the spins of the ith and jth particles, are subsequently constructed. These ‘anyon-like’ representations interestingly lead to different variants of the spin Calogero-Sutherland model with highly non-local interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon-like representations.     

The symmetry of the Hubbard model

The spectrum of the Hubbard model shows permanent degeneracy of levels with different symmetries, if one considers only symmetry operators independent of the coupling constant. This suggests the existence of symmetry operators which depend on the coupling constant. We find these highly nontrivial operators and show that they explain the degeneracies in the energy spectrum.Part of project No. P5588 of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich.     

Multiparameter deformed and non-standard Y(glM) Yangian symmetry in a novel class of spin Calogero-Sutherland models

It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with M internal degrees of freedom, respects the Y(gl_M) Yangian symmetry. By following and suitably modifying the approach of BGHP, in this article we construct a novel class of spin CS models which exhibit multiparameter deformed or ‘non-standard’ variants of Y(gl_M) Yangian symmetry. An interesting feature of such CS Hamiltonians is that they contain many-body spin-dependent interactions, which can be calculated directly from the associated rational solutions of the Yang-Baxter equation. Moreover, these spin-dependent interactions often lead to ‘anyon-like’ representations of the permutation algebra on the combined internal space of all particles. We also find the general forms of conserved quantities as well as Lax pairs for the above-mentioned class of spin CS models, and describe the method of constructing their exact wave functions.     

具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)_L×SU(2)_R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下, 关键词： 中微子质量 轻子味混合矩阵 左右对称模型 代对称性     

Anderson localization and non-linear sigma model with graded symmetry

A model of disordered single-particle systems is studied with regard to properties of the localized phase. Defined over a graded coset space, this model represents the correct non-perturbative extension of a non-linear sigma model introduced into localization theory by Schäfer and Wegner. An integral theorem is proven which allows us to change variables and execute the Grassmann integrations rather easily. In the localized phase, the invariant two-point functions are singular on the real axis. It is shown how to extract the singular contribution before evaluation of the functional integral. This is used to derive Efetov's solution of the Cayley tree model in a simple and transparent manner. Finally, a Monte Carlo algorithm is outlined which makes it possible to study Anderson localization in d > 2 dimensions.