Low-energy modes of spin-imbalanced Fermi gases in BCS phase

The low-energy modes of a spin-imbalanced superfluid Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) side are studied. The gas is assumed to be sufficiently dilute so that the pairing of atoms can be considered effective only in s-wave between fermions of different internal state. The order parameter at equilibrium is determined by the mean-field approximation, while the properties of the collective modes are calculated within a Gaussian approximation for the fluctuations of the order parameter. In particular we investigate the effects of asymmetry between the populations of the two different components and of temperature on the frequency and damping of collective modes. It is found that the temperature does not much affect the frequency and the damping of the modes, whereas an increase of the imbalance shifts the frequency toward lower values and enhances the damping sensitively. Besides the Bogoliubov-Anderson phonons, we observe modes at zero frequency for finite values of the wave-number. These modes indicate that an instability develops driving the system toward two separate phases, normal and superfluid.Comment: 7 pages, 4 figures, submitted to European Physical Journal D for publicatio

The effect of internal and global modes on the radial distribution function of confined semiflexible polymers

The constraints imposed by nano- and microscale confinement on the conformational degrees of freedom of thermally fluctuating biopolymers are utilized in contemporary nano-devices to specifically elongate and manipulate single chains. A thorough theoretical understanding and quantification of the statistical conformations of confined polymer chains is thus a central concern in polymer physics. We present an analytical calculation of the radial distribution function of harmonically confined semiflexible polymers in the weakly bending limit. Special emphasis has been put on a proper treatment of global modes, i.e. the possibility of the chain to perform global movements within the channel. We show that the effect of these global modes significantly impacts the chain statistics in cases of weak and intermediate confinement. Comparing our analytical model to numerical data from Monte Carlo simulations we find excellent agreement over a broad range of parameters.Comment: 6 pages, 3 figures typo corrected, slightly revised line of reasoning, results unchange

Quantum mechanical calculations of rotational-vibrational scattering in homonuclear diatom-atom collisions

Most calculations of the vibrational scattering of diatom-atom collisions use the breathing sphere approximation (BSA) of orientation averaging the intermolecular potential. The resulting angularly symmetric potential can not cause rotational scattering. We determine the error introduced by the BSA into observables of the vibrational scattering of low-energy homonuclear diatom-atom collisions by comparing two quantum mechanical calculations, one with the BSA and the other with the full angularly asymmetric intermolecular potential. For ·reasons of economy the rotational scattering of the second calculation is restricted by the use of special incomplete channel sets in the expansion of the scattering wavefunction. Three representative collision systems are studied: H_2-Ar, O_2-He, and I_2-He. From our calculations, we reach two conclusions. First, the BSA can be used to analyze accurately experimental measurements of vibrational scattering. Second, measurements most sensitive to the symmetric part of the intermolecular potential are, in order, elastic cross sections, inelastic cross sections, and inelastic differential cross sections. Elastic differential cross sections are sensitive to the potential only if the collision is "sticky," with scattering over a wide range of angles; I_2-He is such a collision. Otherwise the potential sensitivity of elastic differential cross sections is concentrated in the experimentally difficult region of very small angle scattering

The Theory of Scanning Quantum Dot Microscopy

Electrostatic forces are among the most common interactions in nature and omnipresent at the nanoscale. Scanning probe methods represent a formidable approach to study these interactions locally. The lateral resolution of such images is, however, often limited as they are based on measuring the force (gradient) due to the entire tip interacting with the entire surface. Recently, we developed scanning quantum dot microscopy (SQDM), a new technique for the imaging and quantification of surface potentials which is based on the gating of a nanometer-size tip-attached quantum dot by the local surface potential and the detection of charge state changes via non-contact atomic force microscopy. Here, we present a rigorous formalism in the framework of which SQDM can be understood and interpreted quantitatively. In particular, we present a general theory of SQDM based on the classical boundary value problem of electrostatics, which is applicable to the full range of sample properties (conductive vs insulating, nanostructured vs homogeneously covered). We elaborate the general theory into a formalism suited for the quantitative analysis of images of nanostructured but predominantly flat and conductive samples

Chemistry of the Spring Waters of the Ouachita Mountains Excluding Hot Springs, Arkansas

This report is based on the chemical analysis of the waters from 93 springs and 9 wells. Springs, when free from metal plumbing, provide an uncontaminated source of the ground water and it was desired to obtain water uncontaminated with metals. A few wells were added to the list, usually because of their unique location in the sampling grid

Errors in Hellmann-Feynman Forces due to occupation number broadening, and how they can be corrected

In ab initio calculations of electronic structures, total energies, and forces, it is convenient and often even necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a boardening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics (MD) calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the (111)-surfaces of aluminium and platinum. The second, more general, scheme employs linear-response theory and is applied to the calculation of the surface relaxation of Al(111). We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton.Comment: 6 pages, 5 figures, Scheduled tentatively for the issue of Phys. Rev. B 15 15 Dec 97 Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm