Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations. Communicated by Vincent Rivasseau Submitted: January 4, 2006 Accepted: January 31, 2006     

Renormalization of the 2-Point Function of the Hubbard Model at Half-Filling

We prove that the Hubbard model at finite temperature T and half-filling is analytic in its coupling constant λ for where c is some numerical constant. We also bound the self-energy and prove that the Hubbard model at half-filling is not a Fermi liquid (in the mathematically precise sense of Salmhofer), modulo a simple lower bound on the first non-trivial self-energy graph, which will be published in a companion paper.submitted 09/09/04, accepted 20/12/04     

Wannier Representation for the Three-Band Hubbard Model

We obtain the cell representation for the Hamiltonian of the d–p model. We use the Wannier orbitals for the holes belonging to the copper and oxygen ions; the orbitals are orthogonalized on the sites of the copper lattice. The first stage of calculating is diagonalizing the kinetic energy of the oxygen holes and, on this basis, introducing two diagonalizing orbitals for the oxygen fermions. These last two modes have significantly different local energies, which noticeably affect the results in the theory. The obtained Hamiltonian is represented as the sum of a main local term and a perturbation defining the delocalization of the Wannier fermions. We find the low-lying states and the corresponding energy spectrum for the local Hamiltonian. We show that introducing the diagonalizing fermions causes a significant lowering of the energy of the Zhang–Rice singlet.     

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??The multivariate response is commonly seen in longitudinal and cross-sectional design. The marginal model is an important tool in discovering the average influence of the covariates on the response. A main feature of the marginal model is that even without specifying the inter-correlation among different components of the response, we still get consistent estimation of the regression parameters. This paper discusses the GMM estimation of marginal model when the covariates are missing at random. Using the inverse probability weighting and different basic working correlation matrices, we obtain a series of estimating equations. We estimate the parameters of interest by minimizing the corresponding quadratic inference function. Asymptotic normality of the proposed estimator is established. Simulation studies are conducted to investigate the finite sample performance of the new estimator. We also apply our proposal to a real data of mathematical achievement from middle school students.     

Chiral fermions in d=11 supergravity with additional time dimensions

Kovrov Branch, Vladimir Polytechnic Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 76, No. 1, pp. 78–87, July, 1988.     

q-Symmetry in Condensed Matter Physics: an Effective Generalized Hubbard Model with Quantum Symmetry

Using the generalized LangFirsov transformation, we reduce the Hubbard model with phonons (which, under particular circumstances, has recently been shown to exhibit the quantum symmetry su(2)[su(2)]_q into an effective electron Hamiltonian. The effective Hamiltonian is explicitly proved to maintain the quantum symmetry, which survives even when relaxing one of the constraints on the Hamiltonian parameters that must hold in the model with phonons. We investigate under which circumstances some superconducting eigenstates of the effective Hamiltonian, which can be built thanks to the quantum symmetry, could become metastable. Bibliography: 12 titles.     

Eigenvalues of the Transfer Matrix of the Three-Dimensional Ising Model in the Particular Case n = m = 2

Theoretical and Mathematical Physics - The 16th-order transfer matrix of the three-dimensional Ising model in the particular case n = m = 2 (n × m is number of spins in a layer) is specified...     

On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source

We investigate the effect of cut-off logistic source on evolutionary dynamics of a generalized Cahn-Hilliard (CH) equation in this paper. It is a well-known fact that the maximum principle does not hold for the CH equation. Therefore, a generalized CH equation with logistic source may cause the negative concentration blow-up problem in finite time. To overcome this drawback, we propose the cut-off logistic source such that only the positive value greater than a given critical concentration can grow. We consider the temporal profiles of numerical results in the one-, two-, and three-dimensional spaces to examine the effect of extra mass source. Numerical solutions are obtained using a finite difference multigrid solver. Moreover, we perform numerical tests for tumor growth simulation, which is a typical application of generalized CH equations in biology. We apply the proposed cut-off logistic source term and have good results.     

Asymptotic Behaviour for a Phase-Field Model with Hysteresis in One-Dimensional Thermo-Visco-Plasticity

The asymptotic behaviour for t of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators.     

Logarithmic corrections in the one-dimensional Hubbard model with attraction

The free energy in the vicinity of a half-filled band for the one-dimensional Hubbard model with attraction is calculated as a function of density (chemical potential). The expansion of the elementary excitation energies for a lattice of finite length N is accomplished with an accuracy of the order (N² ln N)^–1. An explicit expression for the free energy and the elementary excitation spectrum as functions of external field or of volume N is necessary for studying the asymptotic behavior of correlation functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 24–36, 1991.     

Functional approach to the investigation of collective excitations in homogeneous Fermi systems at T=0

A scheme for the investigation of low-energy collective excitations in homogeneous Fermi systems in the functional integral formalism is proposed. It is shown that the spectrum of collective excitations at T=0 is given by the Landau zero-sound dispersion equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 28–33, 1983.     

Exponential Decay of Equal-Time Four-Point Correlation Functions in the Hubbard Model on the Copper-Oxide Lattice

For the Hubbard model on the two-dimensional copper-oxide lattice, equal-time four-point correlation functions at positive temperature are proved to decay exponentially in the thermodynamic limit if the magnitude of the on-site interactions is smaller than some power of temperature. This result especially implies that the equal-time correlation functions for singlet Cooper pairs of various symmetries decay exponentially in the distance between the Cooper pairs in high temperatures or in low-temperature weak-coupling regimes. The proof is based on a multi-scale integration over the Matsubara frequency.     

一类具有脉冲免疫传染病模型SIVS的全局稳定性

讨论了一类具有脉冲免疫的媒介传播的SⅣS流行病模型.疾病的进程依赖感染年龄,时刻t传染率受时刻t-τ媒介种群的影响.模型存在一无病周期解.分析表明存在依赖于脉冲周期和脉冲免疫比例的基本再生数R_0(p,T),当R_0(p,T)<1时,无病周期解是全局稳定的.     

Behaviour of holomorphic automorphisms on equicontinuous subsets of the space

Consider a compact Hausdorff topological space , a -triple and , the -triple of all continuous -valued functions with the pointwise operations and the norm of the supremum. Let be the group of all holomorphic automorphisms of the unit ball of that map every equicontinuous subset lying strictly inside into another such a set. The real Banach-Lie group and its Lie algebra are investigated. The identity connected component of is identified when has the strong Banach-Stone property. This extends to the infinite dimensional setting a well known result concerning the case .