Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The LDOS distribution is found to have the logarithmically normal asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D sample, the result is confirmed by the exact solution. In 2D case a perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotics is of somewhat different type: P(\rho)\sim \exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure

Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots

We study fluctuations of the local density of states (LDOS) on a tree-like lattice with large branching number $m$. The average form of the local spectral function (at given value of the random potential in the observation point) shows a crossover from the Lorentzian to semicircular form at $\alpha\sim 1/m$, where $\alpha= (V/W)^2$, $V$ is the typical value of the hopping matrix element, and $W$ is the width of the distribution of random site energies. For $\alpha>1/m^2$ the LDOS fluctuations (with respect to this average form) are weak. In the opposite case, $\alpha<1/m^2$, the fluctuations get strong and the average LDOS ceases to be representative, which is related to the existence of the Anderson transition at $\alpha_c\sim 1/(m^2\log^2m)$. On the localized side of the transition the spectrum is discrete, and LDOS is given by a set of $\delta$-like peaks. The effective number of components in this regime is given by $1/P$, with $P$ being the inverse participation ratio. It is shown that $P$ has in the transition point a limiting value $P_c$ close to unity, $1-P_c\sim 1/\log m$, so that the system undergoes a transition directly from the deeply localized to extended phase. On the side of delocalized states, the peaks in LDOS get broadened, with a width $\sim\exp\{-{const}\log m[(\alpha-\alpha_c)/\alpha_c]^{-1/2}\}$ being exponentially small near the transition point. We discuss application of our results to the problem of the quasiparticle line shape in a finite Fermi system, as suggested recently by Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section VII added. Accepted for publication in Phys. Rev.

Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte

BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections 5, 7.1, 7.2 with examples, conclusion with all basic results unchanged, corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164), added Refs. 52, 53, 54, examples for massive fields developed by 2 way

Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.Comment: 26 pages, LaTex, 9 PS figures include

Raman scattering studies of spin, charge, and lattice dynamics in Ca_{2-x}Sr_{x}RuO_{4} (0 =< x < 0.2)

We use Raman scattering to study spin, charge, and lattice dynamics in various phases of Ca_{2-x}Sr_{x}RuO_{4}. With increasing substitution of Ca by Sr in the range 0 =< x < 0.2, we observe (1) evidence for an increase of the electron-phonon interaction strength, (2) an increased temperature-dependence of the two-magnon energy and linewidth in the antiferromagnetic insulating phase, and (3) evidence for charge gap development, and hysteresis associated with the structural phase change, both of which are indicative of a first-order metal-insulator transition (T_{MI}) and a coexistence of metallic and insulating components for T < T_{MI}

Magnetotunneling spectroscopy of mesoscopic correlations in two-dimensional electron systems

An approach to experimentally exploring electronic correlation functions in mesoscopic regimes is proposed. The idea is to monitor the mesoscopic fluctuations of a tunneling current flowing between the two layers of a semiconductor double-quantum-well structure. From the dependence of these fluctuations on external parameters, such as in-plane or perpendicular magnetic fields, external bias voltages, etc., the temporal and spatial dependence of various prominent correlation functions of mesoscopic physics can be determined. Due to the absence of spatially localized external probes, the method provides a way to explore the interplay of interaction and localization effects in two-dimensional systems within a relatively unperturbed environment. We describe the theoretical background of the approach and quantitatively discuss the behavior of the current fluctuations in diffusive and ergodic regimes. The influence of both various interaction mechanisms and localization effects on the current is discussed. Finally a proposal is made on how, at least in principle, the method may be used to experimentally determine the relevant critical exponents of localization-delocalization transitions.Comment: 15 pages, 3 figures include

Stock assessment of Queensland east coast saddletail snapper (Lutjanus malabaricus), Australia

In Queensland, east coast saddletail snapper (Lutjanus malabaricus) are mostly line-caught by commercial and recreational fishers, with some recreational spearfishing take. Saddletail snapper are believed to be a single stock (population) off Queensland’s east coast. This is the first stock assessment of the Queensland east coast stock. The assessment implemented a two-sex population model fit to age and length data, constructed within the Stock Synthesis modelling framework. The model incorporated data spanning the period from financial years 1988 to 2020 including commercial logbook harvest (1988–2020), recreational, charter and Indigenous survey harvest estimates (2000–2019), length distribution data from boat-ramp surveys (2017–2020) and age-length (2018–2020). Twenty-one model scenarios were run, covering a wide range of modelling assumptions. Base case (preferred) scenario results suggested that biomass declined between 1961 and 2017 to 19% unfished biomass. In 2020, the stock level was estimated to be 23% (13–73% range across scenarios) unfished biomass. The harvest consistent with a biomass ratio of 60%, the Sustainable Fisheries Strategy longer-term target, was estimated at 159 t (146–348 t range across scenarios and all sectors). The recommended harvest in the 2021 financial year is 12 t (0–494 t range across scenarios) to achieve this target by 2040

On the role of the magnetic dipolar interaction in cold and ultracold collisions: Numerical and analytical results for NH(3Σ−^3\Sigma^-) + NH(3Σ−^3\Sigma^-)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important \textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.Comment: Accepted by Eur. Phys. J. D for publication in Special Issue on Cold Quantum Matter - Achievements and Prospects (2011

Measurement of Bottom versus Charm as a Function of Transverse Momentum with Electron-Hadron Correlations in p+p Collisions at sqrt(s)=200 GeV

The momentum distribution of electrons from semi-leptonic decays of charm and bottom for mid-rapidity |y|<0.35 in p+p collisions at sqrt(s)=200 GeV is measured by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) over the transverse momentum range 2 < p_T < 7 GeV/c. The ratio of the yield of electrons from bottom to that from charm is presented. The ratio is determined using partial D/D^bar --> e^{+/-} K^{-/+} X (K unidentified) reconstruction. It is found that the yield of electrons from bottom becomes significant above 4 GeV/c in p_T. A fixed-order-plus-next-to-leading-log (FONLL) perturbative quantum chromodynamics (pQCD) calculation agrees with the data within the theoretical and experimental uncertainties. The extracted total bottom production cross section at this energy is \sigma_{b\b^bar}= 3.2 ^{+1.2}_{-1.1}(stat) ^{+1.4}_{-1.3}(syst) micro b.Comment: 432 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm