On high-temperature expansions of the Hubbard model

We discuss the application of the high-temperature expansion method to the Hubbard model. We recalculate the expansion series of the susceptibility up to the sixth order in the transfer matrix element,t, in the strong correlation limit, and up to the fourth order int in case that the repulsive potential,U, is finite, butt/U 1. It is seen that the convergence of the series is very poor.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.     

Screened perturbation theory at four loops

We study the thermodynamics of massless ⁴-theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g² and m/T, where m is a thermal mass of order gT. The result is truncated at order g⁷. We find that the convergence properties are significantly improved compared to the weak-coupling expansion.     

Universality of the Break-up Profile for the KdV Equation in the Small Dispersion Limit Using the Riemann-Hilbert Approach

We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation

A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong coupling negativeU Hubbard model

We calculate fluctuation effects on Bose condensation type superconductivity in the strong coupling negative U Hubbard model by means of a new loop expansion. Our method is based on a spin-dependent modification of the Popov-Fedotov trick. We replace the Popov-Fedotov chemical potential by a fictitious imaginary magnetic field. This field is absorbed in spindependent semionic Matsubara frequencies, which allows for a mixed statistics representation of the anisotropic quantum spin 1/2 Heisenberg model. We report results at one loop order for the superconducting order parameter , for the critical temperature, for the chemical potential, and for the excitation spectra both above and belowT _c. We identify mean field results in zeroth loop order and we find both dimensional and filling (v-)depending singularities in interaction fluctuations at one loop order. Renormalization of dimensional singularities is carried out in 4 dimensions. Divergencies withv (1–v)0 in the dilute limits indicate the breakdown of mean field solutions, but superconductivity persists for arbitrarily smallv(1–v) if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma model.     

Nonlinear optimized expansions and the Gross-Neuveu model

An alternative approach to the investigations of the phase structure of the Gross-Neveu model by the optimized expansion method is proposed. Contrary to [6], in order to conserve the Lorentz invariance, the auxiliary scalar fields technique is used. As a result, the interpolation Lagrangian becomes nonlinear in the artificial parameter . The effective potential is constructed by the canonical optimization procedure. The predictions for the phase structure of the model are as in the 1/N expansion method.     

Recoil effect on multiplicity correlation

The kinematical constraint due to energymomentum conservation reduces the multiplicity correlation ine ⁺ e ^–-annihilation (recoil effect). The correction starts at the second order in the expansion in powers of [i.e.O(_s)]. TheO(_s) correction to the squared dispersionr ₂ of the scaled multiplicity distribution is evaluated. It is found so large that the truncated expansion is inadequate at current energies. An evaluation without the expansion gives a reduced correction, with which the prediction remains positive down to low energies. The recoil effect makes the prediction closer to the experimental data.     

A renormalization group analysis of turbulent transport

The field-theoretic renormalization group is used to derive scaling relations for the transport of passive scalars by an incompressible velocity field with a specified energy spectrum. Results are obtained with the analog of the expansion of critical phenomena and compared to exact results which are available for shear flows in two dimensions.A 1/N expansion is proposed for the regions in which the expansion fails.     

Improved Peierls Argument for High-Dimensional Ising Models

We consider the low-temperature expansion for the Ising model on , with ferromagnetic nearest neighbor interactions in terms of Peierls contours. We prove that the expansion converges for all temperatures smaller than Cd(log d)^–1, which is the correct order in d.     

Hubbard-like models in high spatial dimensions

The present paper studies the properties of Hubbard-like models in high spatial dimensionsD. In a first par the limit of infinite dimension and its main features-i.e.i) the mapping onto a generalized atomic model with an additional auxiliary field andii) the validity of the local approximation for the self-energy-are worked out in a systematic (1/D)-expansion. Since the hopping matrix elements have to be properly scaled with the dimensionD, the (1/D)-expansion is also an expansion in the hopping amplitude. Thus for small hopping theD-limit may serve as a proper approximation for finite-dimensional systems. The second part of the paper adopts the hybridisation-perturbation theory of the single impurity Anderson model in order to construct a perturbation theory for the auxiliary field of the generalized atom which can also be interpreted as an expansion in the hopping amplitude. The non-crossing approximation (NCA) is used to study the antiferromagnetic phase transtion of theD-Hubbard model in the case of half filling: the critical temperature, the antiferromagnetic order parameter and the free energy of the lattice system are calculated. The NCA-results are in quite good agreement with recent results from the imaginary-time discretisation method.     

Renormalization of the Chapman–Enskog Expansion: Isothermal Fluid Flow and Rosenau Saturation

This paper continues the author's study of procedures for rewriting the well-known Chapman–Enskog expansion used in the kinetic theory of gases. The usual Chapman–Enskog expansion, when used in isothermal fluid motion, will introduce nonlinear instability at super-Burnett order O(³) truncation. The procedure given here eliminates the truncation instability and produces the desired dissipation inequality.     

The adiabatic approximation for quantum spin systems with a spectral gap

Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO( ^–1.     

The infinite time limit for the time-dependent Born-Oppenheimer approximation

We analyze the Schrödinger equation , whereH() is the hamiltonian of the molecular system consisting of nuclei with masses proportional to ^–4 and electrons with masses of order 1. Using the Born-Oppenheimer method we construct the leading order asymptotic expansion to the exact solutions of the equation. We show that if the particles interact through smooth potentials decaying suitably as the distance between particles tends to , then the expansion holds uniformly for all timest[0,). By similar analysis one can show validity of the expansion fort(–,0], thus our results hold for scattering theory.The material in this paper is contained in a dissertation submitted to the faculty of VPI & SU in partial fulfillment of the requirements for the Ph.D. degree.     

Nonanalytic features of the first order phase transition in the Ising model

The absence of the analytic continuation for the free energy near the point of the first order phase transition in thed-dimensional Ising model is proved. It is shown that thermodynamic functions in the metastable phase do not have certain values and can be derived only with an uncertainty. The asymptotic expansion near the point of the phase transition yields the values of thermodynamic functions with the same uncertainty.     

Semileptonic decays ofB mesons into excited charm mesons: Leading order and 1/m c contributions

We use the heavy quark effective theory to investigate the form factors that describe the semileptonic decays of aB meson into excited daughter mesons. For an excited daughter meson with charm, a single form factor is needed at leading order, while five form factors and two dimensionful constants are needed to order 1/m _c in the heavy quark expansion. For non-charmed final states, a total of four form factors are needed at leading order. For the processBD ^* X, four form factors are also needed at leading order.     

The 1/D expansion for low-dimensional classical magnets

The physical characteristics of two-dimensional classical ferro- and antiferro-magnets have been calculated in the whole temperature range by an analytical approach based on the expansion in powers of 1/D, whereD is the number of spin components. This approach works rather well since it yields exact results for antiferromagnetic susceptibility and specific heat atT=0 already in the first order in 1/D and it is consistent with HTSE at high temperatures. For the quantities singular atT=0, such as ferromagnetic susceptibility and correlation length, the 1/D expansion supports their general-D functional form in the low-temperature range obtained by Fukugita and Oyanagi. The critical index calculated in the first order in 1/D proves to be temperature dependent: =20/(D) (=T/T _c ^(MFT) ,T _c ^(MFT) =J ₀/D, J ₀ is the zero Fourier component of the exchange interaction).     

Approximation for shell-model level densities

The maximum entropy approach for the calculation of nuclear shell-model level densities developed in a previous paper is extended to the calculation of terms of higher order inN _k ^–1, whereN _K is the dimension of the shell-model subspaces of interest. We present terms of first and second order inN _k ^–1 , i.e. in the loop expansion, and the corresponding diagrams. We investigate the size of these contributions for several examples. We find that even for subspace dimensions as small as ten, the saddle-point approximation is quite reliable, the leading terms of the loop expansion are small, and the terms of next order are negligible.On leave from Department of Nuclear Physics, Charles University, S-18000 Prague 8, Czechoslovakia     

Weak disorder expansion of the invariant measure for the one-dimensional Anderson model

We show that the formal perturbation expansion of the invariant measure for the Anderson model in one dimension has singularities at all energiesE ₀=2 cos(p/q); we derive a modified expansion near these energies that we show to have finite coefficients to all orders. Moreover, we show that the firstq–3 of them coincide with those of the naive expansion, while there is an anomaly in the (q–2)th term. This also gives a weak disorder expansion for the Liapunov exponent and for the density of states. This generalizes previous results of Kappus and Wegner and of Derrida and Gardner.     

New universal short-time scaling behaviour of critical relaxation processes

We study the critical relaxation properties of Model A (purely dissipative relaxation) starting from a macroscopically prepared initial state characterised by non-equilibrium values for order parameter and correlations. Using a renormalisation group approach we observe that even (macroscopically)early stages of the relaxation process display universal behaviour governed by a new, independent initial slip exponent. For large times, the system crosses over to the well-known long-time relaxation behaviour.The new exponent is calculated toO(²) in =4–d, whered is the spatial dimension of the system. The initial slip scaling form of general correlation and response functions as well as the order parameter is derived, exploiting a short-time operator expansion. The leading scaling behaviour is determined by initial states with sharp values of the order parameter. Non-vanishing correlations generate corrections to scaling.     

ΔS = 0 effective weak chiral Lagrangianfrom the instanton vacuum

We investigate the ΔS = 0 effective chiral Lagrangian from the instanton vacuum. Based on the ΔS = 0 effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order and the next-to-leading order in the 1/N_c expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the 1/N_c expansion for the ΔS = 0 effective weak chiral Lagrangian, while they are in the leading order terms in the ΔS = 1 case. Three different types of form factors are employed and we find that the dependence on the different choices of the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed in the chiral limit. Arrival of the final proofs: 2 December 2005 PACS: 12.40.-y, 14.20.Dh