A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

Territorial Distribution of Soviet Industry in Context of Preparation of USSR for a Major War (Late 1920s — Early 1940s)

The author considers the complex process of preparing the USSR for war in the context of the implementation of “socialist reconstruction” (a term put forward by I. V. Stalin in November 1929), which meant a radical restructuring of the economic sphere and related institutions. The article poses a complex problem that presents a symbiosis of a number of topics — the NEP, industrialization, the construction of socialism in the Stalinist way, preparations for a big war. Comprehending the key trends in the evolution of the modernization breakthrough of the late 1920s — early 1940s, the author points to two stages. The first (actually continuing the NEP) was dominated by the principles of the planned use of resources, the content of the second was reduced to the next assault on socialism. The researcher comes to the conclusion that the damage caused to the national economy turned out to be significant and became the reason for the disproportionality of its development. The document presents evidence of the fallacy of the territorial organization of heavy industry and, above all, the military-defense complex on the eve of June 22, 1941. The cause of the catastrophe of the first period of the Great Patriotic War is revealed in the loss of the most important enterprises located mainly in areas close to the western border