Two types of electronic states in one dimensional crystals of finite length

Exact and general results on the electronic states in one dimensional crystals bounded at tau and tau+L - where L=Na, N is a positive integer and a is the potential period - are presented. Corresponding to each energy band of Bloch wave, there are N-1 states in the finite crystal and their energies are dependent on the crystal length L but not on the crystal boundary tau and map the energy band exactly; There is always one and only one electronic state correponding to each band gap of the Bloch wave, whose energy is dependent on the crystal boundary tau but not on the crystal length L. This state is either a constant energy confined state at a band edge or a surface state in the gap. A slight change of the boundary tau could change the property and energy of this state dramaticaly.Comment: 17 pages, 3 figure

Language of Lullabies: The Russification and De-Russification of the Baltic States

This article argues that the laws for promotion of the national languages are a legitimate means for the Baltic states to establish their cultural independence from Russia and the former Soviet Union

First-Principles Study on Structural Properties of GeO2_2 and SiO2_2 under Compression and Expansion Pressure

The detailed analysis of the structural variations of three GeO$_2$ and SiO$_2$ polymorphs ($\alpha$-quartz, $\alpha$-cristobalite, and rutile) under compression and expansion pressure is reported. First-principles total-energy calculations reveal that the rutile structure is the most stable phase among the phases of GeO$_2$, while SiO$_2$ preferentially forms quartz. GeO$_4$ tetrahedras of quartz and cristobalite GeO$_2$ phases at the equilibrium volume are more significantly distorted than those of SiO$_2$. Moreover, in the case of quartz GeO$_2$ and cristobalite GeO$_2$, all O-Ge-O bond angles vary when the volume of the GeO$_2$ bulk changes from the equilibrium point, which causes further deformation of tetrahedra. In contrast, the tilt angle formed by Si-O-Si in SiO$_2$ markedly changes. This flexibility of the O-Ge-O bonds reduces the stress at the Ge/GeO$_2$ interface due to the lattice-constant mismatch and results in the low defective interface observed in the experiments [Matsubara \textit{et al.}: Appl. Phys. Lett. \textbf{93} (2008) 032104; Hosoi \textit{et al.}: Appl. Phys. Lett. \textbf{94} (2009) 202112].Comment: 15 pages, 5 figures and 2 table

Theory of strongly correlated f and d-electron systems. I. Exact Hamiltonian, Hubbard-Anderson models and perturbation theory near atomic limit within non-orthogonal basis set

The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym-Kadanoff method for correlated systems.Comment: 40 pages, 6 figure

Bundling up carbon nanotubes through Wigner defects

We show, using ab initio total energy density functional theory, that the so-called Wigner defects, an interstitial carbon atom right besides a vacancy, which are present in irradiated graphite can also exist in bundles of carbon nanotubes. Due to the geometrical structure of a nanotube, however, this defect has a rather low formation energy, lower than the vacancy itself, suggesting that it may be one of the most important defects that are created after electron or ion irradiation. Moreover, they form a strong link between the nanotubes in bundles, increasing their shear modulus by a sizeable amount, clearly indicating its importance for the mechanical properties of nanotube bundles.Comment: 5 pages and 4 figure