Grafted Rods: A Tilting Phase Transition

A tilting phase transition is predicted for systems comprising rod like molecules which are irreversibly grafted to a flat surface, so that the non interacting rods are perpendicularly oriented. The transition is controlled by the grafting density $\rho$. It occurs as $\rho$ increases as a result of the interplay between two energies. Tilt is favoured by the van-der-Waals attraction between the rods. It is opposed by the bending elasticity of the grafting functionality. The role of temperature is discussed, and the tilting mechanism is compared to other tilting transitions reported in the literature.Comment: 21 pages, 2 figures, to appear in Journal de Physique I

Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials

We investigate the possibility of a strongly correlated Fractional Quantum Hall (FQH) state in bulk three dimensional isotropic (not layered) materials. We find that a FQH state can exist at low densities only if it is accompanied by a staging transition in which the electrons re-organize themselves in layers, perpendicular to the magnetic field, at distances of order the magnetic length apart. The Hartree energy associated to the staging transition is off-set by the correlation Fock energy of the 3D FQH state. We obtain the phase diagram of bulk electrons in a magnetic field subject to Coulomb interactions as a function of carrier density and lattice constant. At very low densities, the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilized by phonon correlations

Anti-Fall: A Non-intrusive and Real-time Fall Detector Leveraging CSI from Commodity WiFi Devices

Fall is one of the major health threats and obstacles to independent living for elders, timely and reliable fall detection is crucial for mitigating the effects of falls. In this paper, leveraging the fine-grained Channel State Information (CSI) and multi-antenna setting in commodity WiFi devices, we design and implement a real-time, non-intrusive, and low-cost indoor fall detector, called Anti-Fall. For the first time, the CSI phase difference over two antennas is identified as the salient feature to reliably segment the fall and fall-like activities, both phase and amplitude information of CSI is then exploited to accurately separate the fall from other fall-like activities. Experimental results in two indoor scenarios demonstrate that Anti-Fall consistently outperforms the state-of-the-art approach WiFall, with 10% higher detection rate and 10% less false alarm rate on average.Comment: 13 pages,8 figures,corrected version, ICOST conferenc

Broken symmetry, excitons, gapless modes and topological excitations in Trilayer Quantum Hall systems

We study the interlayer coherent incompressible phase in Trilayer Quantum Hall systems (TLQH) at total filling factor $\nu_{T}=1$ from three approaches: Mutual Composite Fermion (MCF), Composite Boson (CB) and wavefunction approach. Just like in Bilayer Quantum Hall system, CB approach is superior than MCF approach in studying TLQH with broken symmetry. The Hall and Hall drag resistivities are found to be quantized at $h/e^{2}$. Two neutral gapless modes with linear dispersion relations are identified and the ratio of the two velocities is close to $\sqrt{3}$. The novel excitation spectra are classified into two classes: Charge neutral bosonic 2-body bound states and Charge $\pm 1$ fermionic 3-body bound states. In general, there are two 2-body Kosterlize-Thouless (KT) transition temperatures and one 3-body KT transition. The Charge $\pm 1$ 3-body fermionic bound states may be the main dissipation source of transport measurements. The broken symmetry in terms of $SU(3)$ algebra is studied. The structure of excitons and their flowing patterns are given. The coupling between the two Goldstone modes may lead to the broadening in the zero-bias peak in the interlayer correlated tunnelings of the TLQH. Several interesting features unique to TLQH are outlined. Limitations of the CB approach are also pointed out.Comment: 10 pages, 3 figures, Final version to be published in Phys. Rev.

Microscopic analytical theory of a correlated, two-dimensional N-electron gas in a magnetic field

We present a microscopic, analytical theory describing a confined N-electron gas in two dimensions subject to an external magnetic field. The number of electrons N and strength of the electron-electron interaction can be arbitrarily large, and all Landau levels are included implicitly. A possible connection with the Integer and Fractional Quantum Hall Effects is proposed.Comment: The revised version contains minor changes to text. To be published in J. Phys: Condens. Mat

Stacking Faults, Bound States, and Quantum Hall Plateaus in Crystalline Graphite

We analyze the electronic properties of a simple stacking defect in Bernal graphite. We show that a bound state forms, which disperses as |\bfk-\bfK|^3 in the vicinity of either of the two inequivalent zone corners \bfK. In the presence of a strong c-axis magnetic field, this bound state develops a Landau level structure which for low energies behaves as E\nd_n\propto |n B|^{3/2}. We show that buried stacking faults have observable consequences for surface spectroscopy, and we discuss the implications for the three-dimensional quantum Hall effect (3DQHE). We also analyze the Landau level structure and chiral surface states of rhombohedral graphite, and show that, when doped, it should exhibit multiple 3DQHE plateaus at modest fields.Comment: 19 page

The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy

The CDW Hartree-Fock state at half filling and half electron per unit cell is examined. Firstly, an exact solution in terms of Bloch-like states is presented. Using this solution we discuss the dynamics near half filling and show the mass to diverge logarithmically as this filling is approached. We also show how a uniform density state may be constructed from a linear combination of two degenerate solutions. Finally we show the second order correction to the energy to be an order of magnitude larger than that for competing CDW solutions with one electron per unit cell.Comment: 14 pages, no figures, extended acknowledgements, two new references include

Tunneling effect on composite fermion pairing state in bilayer quantum Hall system

We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at \nu=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.

The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. Moreover, we present explicit examples for each one of these cases.Comment: 8 pages, one reference update