Mott transition at large orbital degeneracy: dynamical mean-field theory

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears (Uc1) and the one at which the metal becomes unstable (Uc2) have different dependence on the number of orbitals as the latter becomes large: Uc1 ~ \sqrt{N} while Uc2 ~ N. An exact analytical determination of the critical coupling Uc2/N is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.Comment: 13 pages. Minor changes in V

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Serializing the Parallelism in Parallel Communicating Pushdown Automata Systems

We consider parallel communicating pushdown automata systems (PCPA) and define a property called known communication for it. We use this property to prove that the power of a variant of PCPA, called returning centralized parallel communicating pushdown automata (RCPCPA), is equivalent to that of multi-head pushdown automata. The above result presents a new sub-class of returning parallel communicating pushdown automata systems (RPCPA) called simple-RPCPA and we show that it can be written as a finite intersection of multi-head pushdown automata systems

Transfer of Spectral Weight in Spectroscopies of Correlated Electron Systems

We study the transfer of spectral weight in the photoemission and optical spectra of strongly correlated electron systems. Within the LISA, that becomes exact in the limit of large lattice coordination, we consider and compare two models of correlated electrons, the Hubbard model and the periodic Anderson model. The results are discussed in regard of recent experiments. In the Hubbard model, we predict an anomalous enhancement optical spectral weight as a function of temperature in the correlated metallic state which is in qualitative agreement with optical measurements in $V_2O_3$. We argue that anomalies observed in the spectroscopy of the metal are connected to the proximity to a crossover region in the phase diagram of the model. In the insulating phase, we obtain an excellent agreement with the experimental data and present a detailed discussion on the role of magnetic frustration by studying the $k-$resolved single particle spectra. The results for the periodic Anderson model are discussed in connection to recent experimental data of the Kondo insulators $Ce_3Bi_4Pt_3$ and $FeSi$. The model can successfully explain the different energy scales that are associated to the thermal filling of the optical gap, which we also relate to corresponding changes in the density of states. The temperature dependence of the optical sum rule is obtained and its relevance for the interpretation of the experimental data discussed. Finally, we argue that the large scattering rate measured in Kondo insulators cannot be described by the periodic Anderson model.Comment: 19 pages + 29 figures. Submitted to PR

Zero-temperature magnetism in the periodic Anderson model in the limit of large dimensions

We study the magnetism in the periodic Anderson model in the limit of large dimensions by mapping the lattice problem into an equivalent local impurity self-consistent model. Through a recently introduced algorithm based on the exact diagonalization of an effective cluster hamiltonian, we obtain solutions with and without magnetic order in the half-filled case. We find the exact AFM-PM phase boundary which is shown to be of $2^{nd}$ order and obeys $\frac{V^2}{U} \approx const.$ We calculate the local staggered moments and the density of states to gain insights on the behavior of the AFM state as it evolves from itinerant to a local-moment magnetic regimeComment: 9 pages + 9 figures, to appear in Phys. Rev. B, 1 Sept. 1995 issu

Optical Conductivity in Mott-Hubbard Systems

We study the transfer of spectral weight in the optical spectra of a strongly correlated electron system as a function of temperature and interaction strength. Within a dynamical mean field theory of the Hubbard model that becomes exact in the limit of large lattice coordination, we predict an anomalous enhancement of spectral weight as a function of temperature in the correlated metallic state and report on experimental measurements which agree with this prediction in $V_2O_3$. We argue that the optical conductivity anomalies in the metal are connected to the proximity to a crossover region in the phase diagram of the model.Comment: 12 pages and 4 figures, to appear in Phys. Rev. Lett., v 75, p 105 (1995

Integration of the problem of medical ecology on the level of the highly urbanized region

The urgency of the analyzed issue is due to the study of the basic issues of medical ecology: the dynamics of demographic indicators, the correlation of somatic and reproductive public health, depending on the influence of physical factors of the urban environment on public health on the basis of medical and geographic mapping. The article aims at the analysis of the environmentally determined disorder of the urbanized territory. The leading approach to the study of the issue of medical ecology is a medical and geographical mapping, which allows identifying the most affordable and common areas of multi-component medical and environmental maps. While analyzing the impact of various aspects of the environment on human health, the priority is given to risk factors that directly lead to the emergence of diseases. The contents of the article may be useful to justify the choice of the rational approach to public health as a redistribution mechanism to reallocate the space of ecological niches. © 2016 Rozenberg et al

Dynamical Mean Field Theory of the Antiferromagnetic Metal to Antiferromagnetic Insulator Transition

We study the antiferromagnetic metal to antiferromagnetic insulator using dynamical mean field theory and exact diagonalization methods. We find two qualitatively different behaviors depending on the degree of magnetic correlations. For strong correlations combined with magnetic frustration, the transition can be described in terms of a renormalized slater theory, with a continuous gap closure driven by the magnetism but strongly renormalized by correlations. For weak magnetic correlations, the transition is weakly first order.Comment: 4 pages, uses epsfig,4 figures,notational errors rectifie