Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model

We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime ($|U|\ll t$) behaves as $\sim \exp (-N_a \Delta_{\infty}/4 t)$ in the extreme limit of $N_a \Delta_{\infty} /t \gg 1$, where $t$ is the hopping amplitude, $U$ is the on-site energy, and $\Delta_{\infty}$ is the gap in the thermodynamic limit. Second, in a finite size system a spin-flip producing unpaired fermions leads to the appearance of solitons with non-zero momenta, which provides an extra (non-exponential) contribution $\delta$. For moderate but still large values of $N_a\Delta_{\infty} /t$, these corrections significantly increase and may become comparable with the $1/N_a$ conformal correction. Moreover, in the case of weak interactions where $\Delta_{\infty}\ll t$, the exponential correction exceeds higher order power law corrections in a wide range of parameters, namely for $N_a\lesssim (8t/\Delta_{\infty})\ln(4t/|U|)$, and so does $\delta$ even in a wider range of $N_a$. For sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite size effects.Comment: 17 pages, 5 figure

Vortex structures in rotating Bose-Einstein condensates

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancelation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.Comment: 17 pages, 12 figures, with addition

Subgap tunneling through channels of polarons and bipolarons in chain conductors

We suggest a theory of internal coherent tunneling in the pseudogap region where the applied voltage is below the free electron gap. We consider quasi 1D systems where the gap is originated by a lattice dimerization like in polyacethylene, as well as low symmetry 1D semiconductors. Results may be applied to several types of conjugated polymers, to semiconducting nanotubes and to quantum wires of semiconductors. The approach may be generalized to tunneling in strongly correlated systems showing the pseudogap effect, like the family of High Tc materials in the undoped limit. We demonstrate the evolution of tunneling current-voltage characteristics from smearing the free electron gap down to threshold for tunneling of polarons and further down to the region of bi-electronic tunneling via bipolarons or kink pairs.Comment: 14 pages, 8 postscript figure

Electrochemical surface treatment of glass by a lead-copper melt

Electrochemical surface treatment of a glass by lead-copper melts was investigated and the contents of the anode elements in the glass were determined. It was shown that the glass colour changes as a function of the treatment time. The variation in the content of lead and copper in the glass was established also as function of the treatment duration. Based on the data obtained a technology for the production of new materials from glass can be developed. The surface of these materials is coloured by the ions of lead and copper

Initial Stage of Star Formation

Abstract In frame of the hydrodynamics wh irlwind mechanis m of b ipolar outflow formation fro m disk system the data of observations of active starburst region a dense molecular cloud of Orion KL in H 2 O maser rad iation is analyzed. It is shown that the theory as a first appro ximation exp lains the basic observant laws of active region, structure accompanying protostar formation: a disk-a b ipolar outflo w, includ ing its mechanis m ejection and self-collimation, excitation maser radiat ion

Analytical stripe phase solution for the Hubbard model

The self-consistent solution for the spin-charge solitonic superstructure in quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of a hole doping. Effects of interchain interactions on the ground state are discussed. Results are used for the interpretation of the observed stripe phases in doped antiferromagnets.Comment: 9 pages, LaTex file, no figure

Project-based method in teaching foreign language for specific purposes

This paper considers the innovative methods of teaching Foreign Language for Specific Purposes. The methods are intensively implemented in teaching 3–4-year students at the Institute of Natural Resources, Tomsk Polytechnic University (TPU), Russia. In particular, the paper presents the international project “Approaching the Arctic” developed in cooperation with NTNU (Norwegian University of Science and Technology), Norway. This paper analyzes the efficiency of the implementation of the project-based method in teaching English for Specific Purposes

Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical Hamiltonians is a realization of an integrable Haldane system. The finite-size spectra of the critical Hamiltonians deviate in their structure from standard predictions by conformal invariance.Comment: 16 pages, to appear in Z. Phys. B, preprint Cologne-94-474

Radiation Generation with an Existing Demonstrator of an Energy Recovery Continuous Wave Superconducting RF Accelerator

Over the past decades, many accelerator laboratories have put much effort into the development of compact energy recovery linac ERL demonstrators to verify various physical and technical aspects of the generation, acceleration, transport and energy recovery of high brightness and high average current electron beams in a superconducting radio frequency SRF linear accelerator. Beyond these goals, the ERL demonstrator also offers unique opportunities to study novel schemes for THz and X ray radiation generation. In this paper, we discuss feasible options for schemes generating THz and X ray radiation at low energy continuous wave CW SRF ERL demonstrators such as the bERLinPro accelerato