Broken Symmetries in the Reconstruction of v=1 Quantum Hall Edges

Spin-polarized reconstruction of the v=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon-Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern-Simons Ginzburg-Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region.Comment: Proceedings of the EP2DS, Ottawa (1999) (submitted to Physica E

Skyrmions in quantum Hall ferromagnets as spin-waves bound to unbalanced magnetic flux quanta

A microscopic description of (baby)skyrmions in quantum Hall ferromagnets is derived from a scattering theory of collective (neutral) spin modes by a bare quasiparticle. We start by mapping the low lying spectrum of spin waves in the uniform ferromagnet onto that of free moving spin excitons, and then we study their scattering by the defect of charge. In the presence of this disturbance, the local spin stiffness varies in space, and we translate it into an inhomogeneus metric in the Hilbert space supporting the excitons. An attractive potencial is then required to preserve the symmetry under global spin rotations, and it traps the excitons around the charged defect. The quasiparticle now carries a spin texture. Textures containing more than one exciton are described within a mean-field theory, the interaction among the excitons being taken into account through a new renormalization of the metric. The number of excitons actually bound depends on the Zeeman coupling, that plays the same role as a chemical potencial. For small Zeeman energies, the defect binds many excitons which condensate. As the bound excitons have a unit of angular momentum, provided by the quantum of magnetic flux left unbalanced by the defect of charge, the resulting texture turns out to be a topological excitation of charge 1. Its energy is that given by the non-linear sigma model for the ground state in this topological sector, i.e. the texture is a skyrmion.Comment: 17 pages, 1 figur

Kondo effect in multielectron quantum dots at high magnetic fields

We present a general description of low temperature transport through a quantum dot with any number of electrons at filling factor $1<\nu <2$. We provide a general description of a novel Kondo effect which is turned on by application of an appropriate magnetic field. The spin-flip scattering of carriers by the quantum dot only involves two states of the scatterer which may have a large spin. This process is described by spin-flip Hubbard operators, which change the angular momentum, leading to a Kondo Hamiltonian. We obtain antiferromagnetic exchange couplings depending on tunneling amplitudes and correlation effects. Since Kondo temperature has an exponential dependence on exchange couplings, quantitative variations of the parameters in different regimes have important experimental consequences. In particular, we discuss the {\it chess board} aspect of the experimental conductance when represented in a grey scale as a function of both the magnetic field and the gate potential affecting the quantum dot

Fermions on the Electroweak String

We construct a simple class of exact solutions of the electroweak theory including the naked $Z$--string and fermion fields. It consists in the $Z$--string configuration ($\phi,Z_\theta$), the {\it time} and $z$ components of the neutral gauge bosons ($Z_{0,3},A_{0,3}$) and a fermion condensate (lepton or quark) zero mode. The $Z$--string is not altered (no feed back from the rest of fields on the $Z$--string) while fermion condensates are zero modes of the Dirac equation in the presence of the $Z$--string background (no feed back from the {\it time} and $z$ components of the neutral gauge bosons on the fermion fields). For the case of the $n$--vortex $Z$--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to $|n|$, while for (massless) neutrinos is $|n|-1$. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of $Z_{0,3},A_{0,3}$) does not enhance the stability of the $Z$--string.Comment: 12 text pages (Latex) and 8 postscript figures in a uuencoded fil

Dynamics of the Compact, Ferromagnetic \nu=1 Edge

We consider the edge dynamics of a compact, fully spin polarized state at filling factor $\nu=1$. We show that there are two sets of collective excitations localized near the edge: the much studied, gapless, edge magnetoplasmon but also an additional edge spin wave that splits off below the bulk spin wave continuum. We show that both of these excitations can soften at finite wave-vectors as the potential confining the system is softened, thereby leading to edge reconstruction by spin texture or charge density wave formation. We note that a commonly employed model of the edge confining potential is non-generic in that it systematically underestimates the texturing instability.Comment: 13 pages, 7 figures, Revte

Density functional theory of the phase diagram of maximum density droplets in two-dimensional quantum dots in a magnetic field

We present a density-functional theory (DFT) approach to the study of the phase diagram of the maximum density droplet (MDD) in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level (LLL) approximation, analytical expressions are derived for the values of the parameters $N$ (number of electrons) and $B$ (magnetic field) at which the transition from the MDD to a ``reconstructed'' phase takes place. The results are then compared with those of full Kohn-Sham calculations, giving thus information about both correlation and Landau level mixing effects. Our results are also contrasted with those of Hartree-Fock (HF) calculations, showing that DFT predicts a more compact reconstructed edge, which is closer to the result of exact diagonalizations in the LLL.Comment: ReVTeX 3.

Edge Theories for Polarized Quantum Hall States

Starting from recently proposed bosonic mean field theories for fully and partially polarized quantum Hall states, we construct corresponding effective low energy theories for the edge modes. The requirements of gauge symmetry and invariance under global O(3) spin rotations, broken only by a Zeeman coupling, imply boundary conditions that allow for edge spin waves. In the generic case, these modes are chiral, and the spin stiffness differs from that in the bulk. For the case of a fully polarized $\nu=1$ state, our results agree with previous Hartree-Fock calculations.Comment: 15 pages (number of pages has been reduced by typesetting in RevTeX); 2 references adde

Classical paths in systems of fermions

We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations of randomly distributed paths that do not interfere between themselves and obey classical Dirac equations. Every physical observable is assigned a time-dependent value on each path in a way that respects the anticommutative algebra between quantum operators and we observe that these values on paths do not necessarily satisfy the usual algebraic relations between classical observables. We use these pseudoclassical paths to define the dynamics of quantum fluctuations in systems of fermions and show that, as we found for systems of bosons, the dynamics of fluctuations of a wide class of observables that we call "collective" observables can be approximately described in terms of classical stochastic concepts. Finally, we apply this formalism to describe the dynamics of local fluctuations of globally conserved fermion numbers.Comment: to appear in Pys. Rev.

Implications of area scaling of quantum fluctuations

Quantum fluctuations of a certain class of bulk operators defined in spatial sub-volumes of Minkowski space-time, have an unexpected area scaling property. We wish to present evidence that such area scaling may be ascribed to a boundary theory. We first highlight the implications of area scaling with two examples in which the boundary area of the spatial regions is not monotonous with their volume. Next, we prove that the covariance of two operators that are restricted to two different regions in Minkowski space scales linearly with their mutual boundary area. Finally, we present an example which demonstrates why this implies an underlying boundary theory.Comment: 12 pages, 5 figure

A randomized phase 2 study of sapanisertib in combination with paclitaxel versus paclitaxel alone in women with advanced, recurrent, or persistent endometrial cancer

Endometrial cancer; Metastatic; RecurrentCàncer d'endometri; Metastàtic; RecurrentCáncer endometrial; Metastásico; RecurrenteObjective This phase 2 study investigated sapanisertib (selective dual inhibitor of mTORC1/2) alone, or in combination with paclitaxel or TAK-117 (a selective small molecule inhibitor of PI3K), versus paclitaxel alone in advanced, recurrent, or persistent endometrial cancer. Methods Patients with histologic diagnosis of endometrial cancer (1–2 prior regimens) were randomized to 28-day cycles on four treatment arms: 1) weekly paclitaxel 80 mg/m2 (days 1, 8, and 15); 2) weekly paclitaxel 80 mg/m2 + oral sapanisertib 4 mg on days 2–4, 9–11, 16–18, and 23–25; 3) weekly sapanisertib 30 mg, or 4) sapanisertib 4 mg + TAK-117 200 mg on days 1–3, 8–10, 15–17, and 22–24. Results Of 241 patients randomized, 234 received treatment (paclitaxel, n = 87 [3 ongoing]; paclitaxel+sapanisertib, n = 86 [3 ongoing]; sapanisertib, n = 41; sapanisertib+TAK-117, n = 20). The sapanisertib and sapanisertib+TAK-117 arms were closed to enrollment after futility analyses. After a median follow-up of 14.4 (paclitaxel) versus 17.2 (paclitaxel+sapanisertib) months, median progression-free survival (PFS; primary endpoint) was 3.7 versus 5.6 months (hazard ratio [HR] 0.82; 95% confidence interval [CI] 0.58–1.15; p = 0.139); in patients with endometrioid histology (n = 116), median PFS was 3.3 versus 5.7 months (HR 0.66; 95% CI 0.43–1.03). Grade ≥ 3 treatment-emergent adverse event rates were 54.0% with paclitaxel versus 89.5% paclitaxel+sapanisertib. Conclusions Our findings support inclusion of chemotherapy combinations with investigational agents for advanced or metastatic disease. The primary endpoint was not met and toxicity was manageable. Trial registration: ClinicalTrials.gov number, NCT02725268Takeda Development Center Americas, Inc., Lexington, MA, USA. This work was supported by funding from Takeda Development Center Americas, Inc. The study was designed by the authors in conjunction with the sponsors. Data were gathered and analyzed by the investigator and the sponsor; all the authors had access to the data. The authors received medical writing support for drafting the manuscript, which was funded by Takeda Pharmaceuticals USA, Inc. Manuscript drafts were reviewed by all authors and the sponsor and all the authors made the decision to submit the manuscript for publication