On the spin fluctuation approach to the anderson and Kondo hamiltonians

The free energy expression of the full Anderson model is derived in a similar way as has been done before for the Kondo model. Use is made of the “asymptotic time approximation” first invented to study the x-ray threshold singularity. Again the procedure leads to a classical Coulomb gas on a ring. The magnetic field is included and plays the role of an electric field for the Coulomb gas. Further it turns out that the “symmetric” Anderson model (2ε _d =?U) is identical to the antiferromagnetic Kondo model. The method and the results suggest the construction of a “polaron” model which in the approximation used is equivalent to the Kondo model as well as the Anderson model. From this a new picture of the “Kondo effect” in terms of spin fluctuations is developed.     

Comments on the electric modulus formalism model and superior alternatives to it for the analysis of the frequency response of ionic conductors

Because of the past and continuing wide usage of the 1973 original modulus formalism (OMF) model for analyzing dispersive frequency-response data of ion-conducting materials, it is important to discuss and demonstrate its theoretical and experimental inadequacies to help avoid its future use and to describe and illustrate important alternatives to it. The OMF fits data with a K1 response model alone, one indirectly derived from stretched-exponential temporal behavior, while the corrected modulus formalism (CMF) involves the composite CK1 model, one that includes in addition a separate free, parallel bulk dielectric parameter, ε_D∞. The crucial error of the OMF approach is its identification of a high-frequency-limiting dielectric constant intrinsic to K1 response and associated entirely with conductive effects, with the full high-frequency-limiting dielectric constant of the material, ε_∞, one that must include the non-ionic, primarily dipolar quantity ε_D∞. Comparison here of OMF fitting results with those of the CMF CK1 model for both an experimental data set and an exact one derived from it demonstrate the incorrectness of the OMF and the virtues of the CK1 alternative. The OMF fitting approach, but not the CMF one, leads to crucial inconsistency between the estimates of its β shape parameter for fits of the data expressed at all immittance levels except those of σ′ and ε″, where it yields the same results as the CK1. Its incorrect β estimates, extensively used in the Ngai coupling model and interpreted as being associated with ion–ion correlations, also lead to erroneous “excess wing” effects in plots of the imaginary part of the data and fit at the modulus level. Further, OMF modulus-level fits yield non-physical estimated values of the characteristic relaxation time of the K1 model. Finally, some possible alternatives to the CK1 model are discussed for situations involving dielectric-system dispersion.     

Mean Lyapunov exponent approach for the helicoidal Peyrard-Bishop model

In this Letter, the ordered and disordered regions of the field variable of an oscillator chain are studied. For this purpose, the mean Lyapunov exponent (MLE) theory is applied to the helicoidal Peyrard-Bishop (hPB) model. Applying mean Lyapunov exponent theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the model shows that, the system is very sensitive to the potential parameters. By analyzing the behavior of the MLE with respect to the harmonic helicoidal coupling (K), it can be found that, it is not possible to set the Morse potential parameters of the hPB model in good qualitative agreement with other experimental and theoretical studies. Furthermore, the results show that the MLE is independent of length of the DNA chain. This achievement is important since it can be used to overcome the computational difficulties.     

The critical exponents of the matrix-valued Gross-Neveu model

We study the large-N limit of the matrix-valued Gross-Neveu model in d > 2 dimensions. The method employed is a combination of the approximate recursion formula of Polyakov and Wilson with the solution to the zero-dimensional large-N counting problem of Makeenko and Zarembo. The model is found to have a phase transition at a finite value for the critical temperature and the critical exponents are approximated by ν = 1/(2(d − 2)) and η = d − 2. We test the validity of the approximation by applying it to the usual vector models where it is found to yield exact results to leading order in 1/N.     

Asymmetric model of the quantum Stackelberg duopoly with incomplete information

Asymmetric model of the quantum Stackelberg duopoly with complete information is more efficient than the symmetric one, since it can overcome the deficiencies encountered in the latter. However, the case of complete information is the simplest one in the game, the cases with incomplete information are more general and practical. Here, we will construct such an asymmetric model with incomplete information, where three different parameters γ, α, and ξ are introduced. The analysis shows that all the advantages of the asymmetric case with complete information are maintained. Besides that, one can better manage the market and optimize the total quantity of the product by choosing proper values of α and γ, according to the obtained uncertainty (ξ) of the incomplete information. What' more, it is also worth noticing that the new model is a general one which can degenerate to the case with complete information and that to the symmetric model.     

Random Matrix Theory and the Anderson Model

This paper is devoted to a discussion of possible strategies to prove rigorously the existence of a metal-insulator Anderson transition for the Anderson model in dimension d≥3. The possible criterions used to define such a transition are presented. It is argued that at low disorder the lowest order in perturbation theory is described by a random matrix model. Various simplified versions for which rigorous results have been obtained in the past are discussed. It includes a free probability approach, the Wegner n-orbital model and a class of models proposed by Disertori, Pinson, and Spencer, Comm. Math. Phys. 232:83–124 (2002). At last a recent work by Magnen, Rivasseau, and the author, Markov Process and Related Fields 9:261–278 (2003) is summarized: it gives a toy modeldescribing the lowest order approximation of Anderson model and it is proved that, for d=2, its density of states is given by the semicircle distribution. A short discussion of its extension to d≥3 follows.     

Investigation of the effective interaction by means of a modified shell model

The effective InteractionU for a shell model with hamiltonianH _m is investigated by means of a “mixed” model with hamiltonianH _m . For this model the Bornv. Neumann expansion of the effective interaction? reduces to its first two terms. Within the finite dimensional function space ? _n used in the shell model calculation the operatorsU and? are exactly equivalent. This is used to show that an energy independent approximation forU- if it is possible at all-is necessarily equal to the residual interaction, i.e. to the difference between nucleon-nucleon interaction and shell model interaction.     

Possible phenomenological implications of the new trajectories on the pion trajectory

We discuss possible phenomenological consequences of the new Regge trajectories recently discovered in the conventional dual model (CDM) and the Neveu-Schwarz model (NSM). The contributions of the new trajectories to the scattering amplitude dominate at large enough momentum transfers in the multi-Regge limit and it is shown that the β_π trajectory of the NSM should be the most easy to detect experimentally.     

On thermodynamics of the two-dimensional Heisenberg ferromagnet

Under general assumptions about the magnon dispersion for the model quoted in the title it is stated that at low temperatures T the specific heat is linear in T and the susceptibility is proportional to exp(const/T).     

Statefinder Diagnostic for Modified Chaplygin Gas with the Sign-Changeable Interaction

Statefinder diagnostic is a useful method which can distinguish one dark energy model from the others. In this paper, we apply this method to the modified Chaplygin gas (MCG) model with the sign-changeable interaction in which the interaction term Q can change its sign from Q<0 to Q>0 as the universe expands. We plot the evolutionary trajectories of this model in the statefinder parameter-planes, and it is found that the coupling constant β plays a significant role from the statefinder viewpoint. Furthermore, we can conclude that the statefinder diagnostic can not only discriminate the model with different coupling constant but also distinguish the model from other dark energy models.     

Optical conductivity in the t − J model

Frequency dependent conductivity σ(ω) is calculated for the t ? J model by applying the memory function technique in terms of the Hubbard operators. The relaxation rate due to electron scattering on spin and charge dynamical fluctuations is calculated and a generalized Drude law for σ(ω) is obtained. For a model with an incoherent spectrum for one-hole excitations we obtain a universal form for frequency dependence of relaxation rate and conductivity in terms of the scaling function γ(ω/kT). The relaxation rate for the t ? J model is quite different from that one for the conventional Hubbard model in the strong coupling limit where it vanishes due to an exact cancellation of the intraband scattering and virtual interband transitions.     

Analysis of inclusive nucleon spectra fromp- andα-induced reactions in the frame of the INDEX model,and implications for stopped π−-induced reactions

The previously published INDEX model is tested for nucleon spectra fromp- andα-induced reactions. The results of two alternative versions, the INCLUSIVE INDEX model and the EXCLUSIVE INDEX model, quite well agree with the data. It is found that in the INCLUSIVE INDEX model three preequilibrium stages are sufficient to describe single- and multi-nucleon emission. The model provides an useful first order estimate of the influence of the finite Fermi energy on particle spectra. This effect is very strong for nucleon induced reactions while forα-induced reactions it can be neglected. The deduced mean-free-path multiplier corroborates the long stated discrepancy between models in which excitons interact independently or not. Using preequilibrium parameters similar to those found for nucleon induced reactions the important branching ratio of contributingnp andpp pairs in stoppedπ ^?-absorption can be determined by INDEX model calculations. Deduced values from publishedn- andp-spectra agree reasonably well with those of other experimental analyses but deviate significantly from microscopic model predictions.     

Decreasing of the finite-size effects through the twisted boundary conditions II

In the large-N limit it is shown that a model with twisted boundary conditions becomes equivalent to the U(N) invariant theory which has a volume N² times larger than the theory with periodic boundary conditions. Even for finite N, it is confirmed that the finite-size effects in the models with twisted boundary conditions rather decrease, compared with the ones with periodic boundary conditions, by performing a Monte Carlo simulation for the two-dimensional SU(3) chiral models.     

Antiferromagnetic phase of the Hubbard model

Hubbard's alloy analogy is applied to the antiferromagnetic phase of the Hubbard model. At large U/W it is found that kT_N ～ W²/U.     

The su(n) Hubbard model

The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I introduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that makes it the natural su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the Hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard Hamiltonian in any dimension.     

A simple solution to the strongCP-problem

We suggest soft breaking of Peccei-Quinn symmetry as a simple solution to the strongCP problem without the presence of the axion. In the context of theSU(2) _L ×U(1) model, it is shown how settingθ _tree=0 keeps θ calculable and, furthermore, extremely small: θ?10^?16. Unlike in the case of the axion the model is free from the cosmological domain wall problem. Possible extension of this idea to grand unification is discussed.     

Effect of single-ion anisotropy on the critical-point properties of the exchange interaction model of ferromagnetism

For the spin S exchange interaction model it is shown that both magnetic field and single-ion anisotropy (D) can be exactly treated. When D → ± ∞ the critical-point parameters of this model are exactly the same as those of the $\text{S}\text{=}\text{1}\text{2}$ Heisenberg model.     

New soluble case of the q-state vertex model

A new solution of the Yang-Baxter equations for the q-state two-dimensional vertex model is found. This solution is valid for arbitrary values of temperature. The partition function of the model is calculated by mapping it on the anisotropic square Ising model.     

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences Zitterbewegung, represents a gauge non-invariant variable in our model. Hence our particle does not experience the undesirable Zitterbewegung. C) In the non-relativistic limit spin is described by three-vector, as it could be expected.