Renormalized perturbation theory flow equations for the Anderson impurity model

We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values \(\tilde \mu = (\tilde \Delta ,\tilde U)\) of the hybridization Δ and Coulomb interaction U of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution of \(\tilde \mu = (\tilde \Delta )\) with Δ. By exploiting the fact that \(\tilde \mu = (\tilde \Delta )\) can be determined analytically in the limit Δ → ∞ we solve the flow equations numerically to obtain estimates for the renormalized parameters in the range 0 <U/πΔ< 3.5.     

Diffusion in a bistable potential

The problem of diffusion of a particle in a bistable potential is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. The potential is modeled as two parabolic wells separated by a parabolic barrier. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells. In the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result.     

Current transport in bistable granular structures

Electrical breakdown in GaAs Schottky diodes creates a granular filamentary structure of submicron dimensions between the contacts. The filament exhibits very fast (<2 nsec) electrical switching between stable resistance states. Irrespective of the contact metal, the filament becomes superconducting when in the low-resistance state. Electron transport in all the resistance states is intergrain tunneling between metallic inclusions and is governed by an activation energy. Switching is not based on metal transport.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

非对称Anderson模型的重整微扰展开

利用Yamada微扰论结合重整微扰方法来计算非对称Anderson模型,得到了局域电子占据数、重整化因子、重整化的局域能级以及重整化参数关于裸参数的展开式.计算了局域电子态密度和低温杂质电导,还计算了磁场对它们的影响,这些结果适用于从弱耦合到强耦合的整个耦合强度区域.由于在哈密顿量中已经将局域能级进行了初步重整,采用的重整微扰方法比Hewson的重整微扰方法更适合于研究非对称Anderson模型. 关键词： 非对称Anderson模型 重整化 磁场     

Control the relaxation properties of the diffuse bistable potential

The purpose of this work is to investigate procedures to control the population dynamics in a bistable potential. We use the solutions of the Fokker–Planck equation for the distribution function corresponding to a bistable potential under action of an external electric field. The control is performed with a piecewise protocol with time independent potentials. This protocol provides to be adequate for this problem, controlling the time necessary to balance of system probabilities. Some trajectories were controlled and the limits of procedure clarified. Nevertheless, with the application of the control protocol we clarify some simple phenomena of the system, associating the application of the external field with the system diffusion coefficient.     

Renormalized trajectory for non-linear sigma model and improved scaling behavior

We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(∞) in two dimensions. For finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models.     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Nucleation theory for a model bistable chemical reaction

The theory of homogeneous nucleation is developed for a model nonlinear bistable chemical reaction driven far from equilibrium (trimolecular Schlögl model). The theory is restricted to the vicinity of the stable/unstable transition, where the nucleation barrier is small but nonvanishing. The nucleation rates are derived for two types of fluctuations: first, fluctuations due to a homogeneous external white noise source, and second, internal chemical fluctuations, described by a reastion-diffusion multivariate master equation. In the white noise case, a Landau-Ginzburg potential can be defined, and the standard nucleation formalism can be applied; this is not true for the internal case and a new result is used. The inhomogeneous chemical fluctuations, due to the coupling between the nonlinear reaction and diffusion, are shown to have an influence on the nucleation rate. Quantitative conditions are also given to evaluate the possibility of homogeneous nucleation in nonlinear chemical systems.     

Directional transport equations for plasmas

The yields of the reactions NUCLEUS (γ,yp xn)²⁴Na have been measured for eleven elements with 13≦Z≦29 at maximum bremsstrahlung energies 100 MeV≦E _{γ max}≦ 1000 MeV. An exponential decrease with increasingZ of the mean cross section calculated from the yield data has been obtained. ThisZ-dependence fits well to the systematics of spallation product cross-sections.     

Coherent transport in a periodically driven bistable system

The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to the driving are investigated numerically and explained in terms of the structure of the corresponding local quasienergy spectrum. In particular, there is a one-dimensional manifold in the parameter space spanned by the amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The quantal dynamics in the semiclassical regime as well as the influence of weak incoherent processes are briefly discussed.     

Renormalized expansions for functional integrals: Generalized coherent potential approach to lattice models

An expansion for generating functionals (partition sums) of models expressed as lattice functional integrals with local (on-site) interactions is presented. This expansion renormalizes the standard perturbative expansion in such a way that certain its terms are summed up non-perturbatively. A non-self-consistent and a self-consistent versions of the expansion are formulated and criteria for an estimation of validity of approximations resulting from the both expansions are given. The simplest approximation being the first term of this expansion is applied to two lattice models: classicalN-component spin model and the model of non-interacting electrons in a disordered crystal. In the former model the critical temperature is calculated within 10% accuracy and in the latter, the coherent potential approximation is obtained.     

Renormalized loop expansion to compute finite size effects of the constraint effective potential

In latticeφ ⁴ close to the critical line, finite size effects can be computed by renormalized loop expansions. In order to do so, the constraint effective potential is computed to two loop order. Using this expression, we are able to extract results for renormalized masses and coupling constants from Multigrid Monte Carlo data of Mack and Meyer for the constraint effective potential close to the critical line, and compare them with the analytical results ofLüscher and Weisz. Perfect agreement is found.     

Renormalized finite temperature effective potential ofSU(2) Yang-Mills theory

It is shown that the renormalized finite temperature effective potential for continuumSU(2) Yang-Mills theory develops a non-perturbative minimum for sufficiently strong coupling, i.e. below a critical temperature. The corresponding phase can be the candidate for the confining phase of the continuum theory and becomes energetically favoured basicly due to the decay of theA ⁰ condensate into three gluons.