Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal ($\sigma_{xx}$) and off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$ with $\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between $\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.Comment: 21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matte

Magnetoroton scattering by phonons in the fractional quantum Hall regime

Motivated by recent phonon spectroscopy experiments in the fractional quantum Hall regime we consider processes in which thermally excited magnetoroton excitations are scattered by low energy phonons. We show that such scattering processes can never give rise to dissociation of magnetorotons into unbound charged quasiparticles as had been proposed previously. In addition we show that scattering of magnetorotons to longer wavelengths by phonon absorption is possible because of the shape of the magnetoroton dispersion curve and it is shown that there is a characteristic cross-over temperature above which the rate of energy transfer to the electron gas changes from an exponential (activated) to a power law dependence on the effective phonon temperature.Comment: LaTex document, 3 eps figures. submitted to Phys Rev

Fermi Edge Singularities in Transport through Quantum Dots

We study the Fermi-edge singularity appearing in the current-voltage characteristics for resonant tunneling through a localized level at finite temperature. An explicit expression for the current at low temperature and near the threshold for the tunneling process is presented which allows to coalesce data taken at different temperatures to a single curve. Based on this scaling function for the current we analyze experimental data from a GaAs-AlAs-GaAs tunneling device with embedded InAs quantum dots obtained at low temperatures in high magnetic fields.Comment: 12 pages, 5 figure

Metallicities of M Dwarf Planet Hosts from Spectral Synthesis

We present the first spectroscopic metallicities of three M dwarfs with known or candidate planetary mass companions. We have analyzed high resolution, high signal-to-noise spectra of these stars which we obtained at McDonald Observatory. Our analysis technique is based on spectral synthesis of atomic and molecular features using recently revised cool-star model atmospheres and spectrum synthesis code. The technique has been shown to yield results consistent with the analyses of solar-type stars and allows measurements of M dwarf [M/H] values to 0.12 dex precision. From our analysis, we find [M/H] = -0.12, -0.32, and -0.33 for GJ 876, GJ 436, and GJ 581 respectively. These three M dwarf planet hosts have sub-solar metallicities, a surprising departure from the trend observed in FGK-type stars. This study is the first part of our ongoing work to determine the metallicities of the M dwarfs included in the McDonald Observatory planet search program.Comment: 13 pages, 2 figures, accepted for publication in ApJ

Localized states in strong magnetic field: resonant scattering and the Dicke effect

We study the energy spectrum of a system of localized states coupled to a 2D electron gas in strong magnetic field. If the energy levels of localized states are close to the electron energy in the plane, the system exhibits a kind of collective behavior analogous to the Dicke effect in optics. The latter manifests itself in ``trapping'' of electronic states by localized states. At the same time, the electronic density of states develops a gap near the resonance. The gap and the trapping of states appear to be complementary and reflect an intimate relation between the resonant scattering and the Dicke effect. We reveal this relation by presenting the exact solution of the problem for the lowest Landau level. In particular, we show that in the absence of disorder the system undergoes a phase transition at some critical concentration of localized states.Comment: 28 pages + 9 fig

Probing the quantum phase transition in the Dicke model through mechanical vibrations

This paper is concerned with quantum dynamics of a system coupled to a critical reservoir. In this context, we employ the Dicke model which is known to exhibit a super radiant quantum phase transition (QPT) and we allow one of the mirrors to move under a linear restoring force. The electromagnetic field couples to the movable mirror though radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the super-radiant phase induces a classical driving force on the mirror without causing decoherence.Comment: 6 pages, 3 figures, final versio

Mapping lung cancer epithelial-mesenchymal transition states and trajectories with single-cell resolution.

Elucidating the spectrum of epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) states in clinical samples promises insights on cancer progression and drug resistance. Using mass cytometry time-course analysis, we resolve lung cancer EMT states through TGFβ-treatment and identify, through TGFβ-withdrawal, a distinct MET state. We demonstrate significant differences between EMT and MET trajectories using a computational tool (TRACER) for reconstructing trajectories between cell states. In addition, we construct a lung cancer reference map of EMT and MET states referred to as the EMT-MET PHENOtypic STAte MaP (PHENOSTAMP). Using a neural net algorithm, we project clinical samples onto the EMT-MET PHENOSTAMP to characterize their phenotypic profile with single-cell resolution in terms of our in vitro EMT-MET analysis. In summary, we provide a framework to phenotypically characterize clinical samples in the context of in vitro EMT-MET findings which could help assess clinical relevance of EMT in cancer in future studies

A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field

We present a solvable model of two-dimensional dilaton-gravity coupled to a massless scalar field. We locally integrate the field equations and briefly discuss the properties of the solutions. For a particular choice of the coupling between the dilaton and the scalar field the model can be interpreted as the two-dimensional effective theory of 2+1 cylindrical gravity minimally coupled to a massless scalar field.Comment: 6 pages, RevTeX, to be published in Phys. Rev.