The fractional quantum Hall effect: Chern-Simons mapping, duality, Luttinger liquids and the instanton vacuum

We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes the effects of disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We introduce a theory of spatially separated (individually conserved) edge modes, find an enlarged dual symmetry and obtain a complete classification of quasiparticle operators and tunneling exponents. The chiral anomaly on the edge and Laughlin's gauge argument are used to obtain unambiguously the Hall conductance. In resolving the problem of counter flowing edge modes, we find that the long range Coulomb interactions play a fundamental role. In order to set up a theory for arbitrary filling fractions $\nu$ we use the idea of a two dimensional network of percolating edge modes. We derive an effective, single mode Luttinger liquid theory for tunneling processes into the quantum Hall edge which yields a continuous tunneling exponent $1/\nu$. The network approach is also used to re-derive the instanton vacuum or $Q$-theory for the plateau transitions.Comment: 36 pages, 7 figures (eps

The problem of Coulomb interactions in the theory of the quantum Hall effect

We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkelstein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry ($\cal F$ invariance) for systems with an infinitely ranged interaction potential. We address the renormalization of the theory and present the main results in terms of a scaling diagram of the conductances.Comment: 9 pages, 3 figures. To appear in Proceedings of the International Conference "Mesoscopics and Strongly Correlated Electron Systems", July 2000, Chernogolovka, Russi

(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results

The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2\epsilon spatial dimensions. We report the results of a detailed renormalization group analysis and establish the renormalizability of the (Finkelstein) action to two loop order. We show that the infrared behavior of the theory can be extracted from gauge invariant (F-invariant) quantities only. For these quantities (conductivity, specific heat) we derive explicit scaling functions. We identify a bosonic quasiparticle density of states which develops a Coulomb gap as one approaches the metal-insulator transition from the metallic side. We discuss the consequences of F-invariance for the strong coupling, insulating regime.Comment: 26 pages, 7 figures; minor modifications; submitted to Phys.Rev.

(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the \nu=1/2 state

We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and Chern-Simons gauge theory. We elaborate on the microscopic origins of the effective action and unravel a new symmetry in the problem with Coulomb interactions which we name F-invariance. This symmetry has a broad range of physical consequences which will be the main topic of future analyses. In the second half of this paper we compute the response of the theory to electromagnetic perturbations at a tree level approximation. This is applicable to the theory of ordinary metals as well as the composite fermion approach to the half-integer effect. Fluctuations in the Chern-Simons gauge fields are found to be well behaved only when the theory is F-invariant.Comment: 20 pages, 6 figures; appendix B revised; submitted to Phys.Rev.

Tardos fingerprinting is better than we thought

We review the fingerprinting scheme by Tardos and show that it has a much better performance than suggested by the proofs in Tardos' original paper. In particular, the length of the codewords can be significantly reduced. First we generalize the proofs of the false positive and false negative error probabilities with the following modifications: (1) we replace Tardos' hard-coded numbers by variables and (2) we allow for independently chosen false positive and false negative error rates. It turns out that all the collusion-resistance properties can still be proven when the code length is reduced by a factor of more than 2. Second, we study the statistical properties of the fingerprinting scheme, in particular the average and variance of the accusations. We identify which colluder strategy forces the content owner to employ the longest code. Using a gaussian approximation for the probability density functions of the accusations, we show that the required false negative and false positive error rate can be achieved with codes that are a factor 2 shorter than required for rigid proofs. Combining the results of these two approaches, we show that the Tardos scheme can be used with a code length approximately 5 times shorter than in the original construction.Comment: Modified presentation of result

Quantum Key Recycling with 8-state encoding (The Quantum One-Time Pad is more interesting than we thought)

Perfect encryption of quantum states using the Quantum One-Time Pad (QOTP) requires two classical key bits per qubit. Almost-perfect encryption, with information-theoretic security, requires only slightly more than 1. We slightly improve lower bounds on the key length. We show that key length n+2log1ε n+2log1ε suffices to encrypt n n qubits in such a way that the cipherstate’s L 1 L1 -distance from uniformity is upperbounded by ε ε . For a stricter security definition involving the ∞ ∞ -norm, we prove sufficient key length n+logn+2log1ε +1+1n log1δ +logln21−ε n+logn+2log1ε+1+1nlog1δ+logln21−ε , where δ δ is a small probability of failure. Our proof uses Pauli operators, whereas previous results on the ∞ ∞ -norm needed Haar measure sampling. We show how to QOTP-encrypt classical plaintext in a nontrivial way: we encode a plaintext bit as the vector ±(1,1,1)∕3 – √ ±(1,1,1)∕3 on the Bloch sphere. Applying the Pauli encryption operators results in eight possible cipherstates which are equally spread out on the Bloch sphere. This encoding, especially when combined with the half-keylength option of QOTP, has advantages over 4-state and 6-state encoding in applications such as Quantum Key Recycling (QKR) and Unclonable Encryption (UE). We propose a key recycling scheme that is more efficient and can tolerate more noise than a recent scheme by Fehr and Salvail. For 8-state QOTP encryption with pseudorandom keys, we do a statistical analysis of the cipherstate eigenvalues. We present numerics up to nine qubits

Intense Reflection of a Relativistic Laser Pulse in Subcritical Plasmas

Interaction of relativistic electromagnetic (EM) (laser) pulse with plasmas has been investigated by means of electromagnetic particle-in-cell simulations. When a relativistic laser pulse, stronger than a critical intensity, is injected into a uniform plasma of sub-critical density (nc/4 < n0/γ < nc), strong reflection is observed. The frequency of the back-scattered wave is near the effective electron plasma frequency which is well below its unperturbed value. This novel stimulated scattering instability is recognized as a three-wave parametric resonance decay of the incident wave into an electron-acoustic wave (EAW) (ω << ωp) and a scattered EM Stokes sideband. The slow Stokes lightwave gradually builds up to eventually propagate through the plasma-vacuum interface in a form of short superintense reflectivity bursts of coherent low-frequency EM radiation

Liberating Technologies? Perceptions of Government Control and Citizens’ Use of Social Media during the Elections

Social media may liberate citizens in societies with stringent media controls and accelerate political democratization. Yet, little is known about the relation between social media use and perceived constraints in a semi-authoritarian system. This study draws on Media System Dependency theory to examine this relation in the context of the 2011 Singapore General Election. Our findings, based on national survey data, suggest that perceived control of traditional media and political activity is positively related to content production on social media as well as the visits to opposition party websites and Facebook pages. Additionally, perceived control of mass media is associated with increased consumption of political content on social media. Perceived control of the Internet reduces rather than increases content production on social media. We argue that social media alters the balance of dependency relationships between the government, media organizations and citizens. They create new, meso level networked avenues for information gathering and participation during the elections

Relationships between leaf traits and morphological attributes in one-year bareroot Fraxinus anguslifolia Vahl. seedlings

Leaf traits were investigated as morphological attributes for quality estimation of one-year-old bareroot seedlings of Fraxinus angustifolia Vahl. Leaf traits (number of simple - NSL and compound leaves - NCL, leaf average - ALA and total area - TLA and leaf area ratio - LAR) show similar relations to morphological attributes, the strongest to shoot growth (height - HT, root collar diameter - DIA and shoot dry weight - SDW). Increases of seedling morphological attributes are strongly related to increases of ALA. Given to strong positive correlations with other morphological attributes, ALA (R = 0.68-0.88) and TLA (R = 0.46-0.92) are suitable for seedlings quality testing. TLA explained a larger proportion of the variation of SDW (R-2 = 0.85) and ALA explained a large proportion of the variation of DIA (R-2 = 0.81). Leaf traits can be considered as valuable morphological attributes of seedling quality, in addition to strong correlation with other morphological attributes

Las implicaciones de ser asocial en las redes sociales

Early research on social media supported some of the optimistic views about their positive impact on social capital and linked their use with the exposure to more diverse views and greater engagement with society. Still, more recently, scholars have started looking into “unsocial” behaviors on social media platforms, such as unfriending, unfollowing and muting, and examining their social capital implications. In this essay, we review the extant research on these selective avoidance and disconnection practices and advance the concept of “digital safe spaces” -online environments created via post-hoc filtering and curation of social ties- to further discuss their role in contemporary democratic societies. We find that digital safe spaces may provide fertile grounds for civic and political expression, particularly for minorities. However, the creation of these digital enclaves may also drive minorities further away from the political mainstream and may lead to the reduction economic and political opportunities for the citizens who are excluded from “safe spaces”.Los primeros estudios sobre redes sociales respaldaban visiones optimistas en relación con su impacto positivo en el desarrollo del capital social, y relacionaban su uso con la exposición a puntos de vista más diversos y a un mayor compromiso con la sociedad. Sin embargo, recientemente, los investigadores empezaron a analizar los comportamientos asociales que se pueden llevar a cabo en las redes sociales y a estudiar sus consecuencias sobre el desarrollo del capital social. En este ensayo, revisamos la literatura existente centrada en estudiar estas prácticas de evitación y desconexión selectiva y avanzamos en el concepto de ‘espacios digitales seguros’ -entornos&nbsp;online&nbsp;creados filtrando y eliminando&nbsp;post hoc&nbsp;a contactos en redes sociales-, con el objetivo de profundizar en el debate sobre sus consecuencias en las sociedades democráticas contemporáneas. Nuestros hallazgos apuntan al hecho de que los espacios digitales seguros pueden constituir un entorno fértil para la expresión cívica y política, especialmente para las minorías. Sin embargo, la creación de estos enclaves digitales puede también alejar aún más a las minorías del consenso político generalizado y podría llevar a una reducción de las oportunidades económicas y políticas de aquellos ciudadanos que están excluidos de los “espacios seguros”