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

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

Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

BERLinPro A Compact Demonstrator ERL for High Current and Low Emittance Beams

The HZB previously BESSY was the first institution in Germany to build and operate a dedicated synchrotron light source BESSY I . About 10 years ago BESSY II, a third generation synchrotron light source, was commissioned and is very successfully running since that time. Due to its expertise in development and operation of accelerator facilities HZB is ideally suited to realize new accelerator concepts. Therefore HZB is proposing to build a demonstrator ERL facility BERLinPro that will realize high current and low emittance operation at 100 MeV. BERLinPro is intented to bring ERL technology to maturity. This paper presents an overview of the project and the key components of the facilit

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

Results from Beam Commissioning of an SRF Plug Gun Cavity Photoinjector

Superconducting rf photo electron injectors SRF photoinjectors hold the promise to deliver high brightness, high average current electron beams for future light sources or other applications demanding continuous wave operation of an electron injector. This paper discusses results from beam commissioning of a hybrid SRF photoinjector based on a Pb coated plug and a Nb rf gun cavity for beam energies up to 2.5MeV at Helmholtz Zentrum Berlin HZB . Emittance measurements and transverse phase space characterization with solenoid scan and slitmask methods will be presente

A 3D view of the outflow in the Orion Molecular Cloud 1 (OMC-1)

The fast outflow emerging from a region associated with massive star formation in the Orion Molecular Cloud 1 (OMC-1), located behind the Orion Nebula, appears to have been set in motion by an explosive event. Here we study the structure and dynamics of outflows in OMC-1. We combine radial velocity and proper motion data for near-IR emission of molecular hydrogen to obtain the first 3-dimensional (3D) structure of the OMC-1 outflow. Our work illustrates a new diagnostic tool for studies of star formation that will be exploited in the near future with the advent of high spatial resolution spectro-imaging in particular with data from the Atacama Large Millimeter Array (ALMA). We use published radial and proper motion velocities obtained from the shock-excited vibrational emission in the H2 v=1-0 S(1) line at 2.122 $\mu$m obtained with the GriF instrument on the Canada-France-Hawaii Telescope, the Apache Point Observatory, the Anglo-Australian Observatory and the Subaru Telescope. These data give the 3D velocity of ejecta yielding a 3D reconstruction of the outflows. This allows one to view the material from different vantage points in space giving considerable insight into the geometry. Our analysis indicates that the ejection occurred <720 years ago from a distorted ring-like structure of ~15" (6000 AU) in diameter centered on the proposed point of close encounter of the stars BN, source I and maybe also source n. We propose a simple model involving curvature of shock trajectories in magnetic fields through which the origin of the explosion and the centre defined by extrapolated proper motions of BN, I and n may be brought into spatial coincidence.Comment: Accepted for publication in Astronomy and Astrophysics (A&A), 12 pages, 9 figure

The level of air pollution in the impact zone of coal-fired power plant (Karaganda City) using the data of geochemical snow survey (Republic of Kazakhstan)

Coal-fired power plants emissions impact the air quality and human health. Of great significance is assessment of solid airborne particles emissions from those plants and distance of their transportation. The article presents the results of air pollution assessment in the zone of coal-fired power plant (Karaganda City) using snow survey. Based on the mass of solid airborne particles deposited in snow, time of their deposition on snow at the distance from 0.5 to 4.5 km a value of dust load has been determined. It is stated that very high level of pollution is observed at the distance from 0.5 to 1 km. there is a trend in decrease of dust burden value with the distance from the stacks of coal-fired power plant that may be conditioned by the particle size and washing out smaller ash particles by ice pellets forming at freezing water vapour in stacks of the coal-fired power plant. Study in composition of solid airborne particles deposited in snow has shown that they mainly contain particulates of underburnt coal, Al-Si- rich spheres, Fe-rich spheres, and coal dust. The content of the particles in samples decreases with the distance from the stacks of the coal-fired power plant