Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study

The Field Induced Spin Density Wave phases observed in quasi-one-dimensional conductors of the Bechgaard salts family under magnetic field exhibit both Spin Density Wave order and a Quantized Hall Effect, which may exhibit sign reversals. The original nature of the condensed phases is evidenced by the collective mode spectrum. Besides the Goldstone modes, a quasi periodic structure of Magneto-Roton modes, predicted to exist for a monotonic sequence of Hall Quantum numbers, is confirmed, and a second mode is shown to exist within the single particle gap. We present numerical estimates of the Magneto-Roton mode energies in a generic case of the monotonic sequence. The mass anisotropy of the collective mode is calculated. We show how differently the MR spectrum evolves with magnetic field at low and high fields. The collective mode spectrum should have specific features, in the sign reversed "Ribault Phase", as compared to modes of the majority sign phases. We investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat preprint cond-mat/9709210, but cannot be described as a replaced version, because it contains a significant amount of new material dealing with the instability line and with the topic of Ribault Phases. It contains 13 figures (.ps files

Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in pressure independent velocity error estimates which are robust with respect to small viscosities. In this paper we develop a posteriori error control which reflects this robustness. The main difficulty lies in the volume contribution of the standard residual-based approach that includes the $L^2$-norm of the right-hand side. However, the velocity is only steered by the divergence-free part of this source term. An efficient error estimator must approximate this divergence-free part in a proper manner, otherwise it can be dominated by the pressure error. To overcome this difficulty a novel approach is suggested that uses arguments from the stream function and vorticity formulation of the Navier--Stokes equations. The novel error estimators only take the $\mathrm{curl}$ of the right-hand side into account and so lead to provably reliable, efficient and pressure-independent upper bounds in case of a pressure-robust method in particular in pressure-dominant situations. This is also confirmed by some numerical examples with the novel pressure-robust modifications of the Taylor--Hood and mini finite element methods

Wavefunctions for the Luttinger liquid

Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the gaussian boson LL hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions.Comment: 5 pages; accepted for publication in EPR B, Rapid Note

Fractional excitations in the Luttinger liquid

We reconsider the spectrum of the Luttinger liquid (LL) usually understood in terms of phonons (density fluctuations), and within the context of bosonization we give an alternative representation in terms of fractional states. This allows to make contact with Bethe Ansatz which predicts similar fractional states. As an example we study the spinon operator in the absence of spin rotational invariance and derive it from first principles: we find that it is not a semion in general; a trial Jastrow wavefunction is also given for that spinon state. Our construction of the new spectroscopy based on fractional states leads to several new physical insights: in the low-energy limit, we find that the $S_{z}=0$ continuum of gapless spin chains is due to pairs of fractional quasiparticle-quasihole states which are the 1D counterpart of the Laughlin FQHE quasiparticles. The holon operator for the Luttinger liquid with spin is also derived. In the presence of a magnetic field, spin-charge separation is not realized any longer in a LL: the holon and the spinon are then replaced by new fractional states which we are able to describe.Comment: Revised version to appear in Physical Review B. 27 pages, 5 figures. Expands cond-mat/9905020 (Eur.Phys.Journ.B 9, 573 (1999)

Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu=4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu=4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.Comment: 4 pages, 3 figures; revised version accepted for publication in Phys. Rev. Let

Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect

A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, such as nu=4/11. Projection of the composite-fermion dynamics to a single level, involved in the derivation of the Hamiltonian of interacting composite fermions, reveals the underlying self-similarity of the model.Comment: 4 pages, 1 figure; to appear in "Proceedings of the 16th International Conference on High Magnetic Fields in Semiconductor Physics (SemiMag-16)", only change with respect to v1: correction in authors line, no changes in manuscrip

Quantum Phases in Partially Filled Landau Levels

We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions between these phases when varying the filling of the top-most partially filled Landau level explain the observed reentrance of the integer quantum Hall effect. The phase transitions are identified as first-order. This leads to a variety of measurable phenomena such as the phase coexistence between a Wigner crystal and a two-electron bubble phase in a Landau-level filling-factor range $4.15 < nu < 4.26$, which has recently been observed in transport measurements under micro-wave irradiation.Comment: 6 pages, 2 figures; to appear in "Proceedings of the 16th International Conference on High Magnetic Fields in Semiconductor Physics (SemiMag-16)

NASAs Orbital Debris JAO/ES-MCAT Optical Telescope Facility on Ascension Island

The NASA Orbital Debris Program Office has a long-standing optical program begun over three and a half decades ago in 1984, designed to observe the Earth-orbiting environment with optical telescopes. Photometrically calibrated optical data provides a statistical sample for input to NASA models of the debris population for understanding the current and future debris environment around the Earth. Tracked objects and orbits allow for analysis of break-up events. Both known (correlated target in the SSN catalogue, or CT) and unknown (uncorrelated target, or UCT) objects are of interest to better understand how to protect current spacecraft and design more robust future operational satellites, and advise on how policies and practices can lead to protecting the environment itself for future generations. In 2015, a joint NASA JSC Air Force Research Labs (AFRL) project culminated in the installation of the 1.3-meter Eugene Stansbery Meter Class Autonomous Telescope, ES-MCAT (a.k.a. MCAT) on Ascension Island. This DFM Engineering designed telescope provides nearly five-times greater light-collecting power than its predecessor, the 0.6-m MODEST telescope, and faster tracking capabilities by both the telescope and the 7-m ObservaDome. This allows for all orbital regimes to be easily within reach, ranging from low Earth to geosynchronous orbits. Extensive testing and commissioning activities of this custom system led to successfully reaching Initial Operational Capability in 2018, and the facility is currently on track to reach Full Operational Capability. The John Africano Observatory (JAO) comprises the primary 1.3-m ES-MCAT facility, the adjacent tower platform with a 0.4-m telescope, a sophisticated suite of weather instruments, and custom software by Euclid Research for autonomously running the entire system, including monitoring the weather and hardware, tasking all components, and collecting, processing, and analyzing the data. The mission of JAO and MCAT will be discussed, including survey and tracking tasking, a full discussion of data calibration, and both optics and weather-dependent performance

Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d$_{x^2-y^2}$-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electron-phonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half-filling the Fermi surface is nested, spin-density-wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.Comment: 8 pages, 5 figure