Narrow Results

We analyze the fluctuations of charge of the (1+1)-dimensional Dirac's fermion with charge conjugation breaking. This is done taking the separation between background soliton and antisoliton going to infinity.

Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter to distinguish different states of matter. Experiments in a number of correlated materials raise serious suspicions about the general validity of either notion. A growing body of theoretical work has confirmed these suspicions, and explored physics beyond Landau's paradigms. This article provides an overview of some of these theoretical developments.

Inequality, asymmetry, and the median-mean ratio are related but different concepts, although they have been frequently treated as equivalent in the literature. In this paper, we find important connections between these three concepts under particular conditions. We show that the Atkinson family and the generalized entropy class of inequality indices are simple functions of the medianmean ratio when a distribution is symmetrizable by a power transformation. In such a case, the coefficient of asymmetry can be interpreted as the aversion inequality parameter of a social planner, and a social evaluation function à la Kolm-Atkinson is shown to be equivalent to median income. A social evaluation function that depends only on mean income and inequality of opportunity is found as a by-product. In addition, the Hannah-Kay family of concentration indices (of which the Herfindahl-Hirschman is a special case) is also obtained as a function of the median-mean ratio. We illustrate these results empirically using the CPS dataset for the U.S. (1992—2007) and the EU-SILC dataset for the European Union (2005–2007).

Using a dataset on 80 poverty pockets in Lebanon in 2004, we find that polarization, fractionalization and sectarian distance consistently and robustly affect a pocket's ability to attract development assistance funds. Our results are consistent with the prerogative of confessional balance in government decisions dictated by the power-sharing game in the post-war era. They put into question the design of effective channels to allocate development funds in polarized societies.

Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter to distinguish different states of matter. Experiments in a number of correlated materials raise serious suspicions about the general validity of either notion. A growing body of theoretical work has confirmed these suspicions, and explored physics beyond Landau's paradigms. This article provides an overview of some of these theoretical developments.

We prove sufficient conditions for Topological Quantum Order (TQO). The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (GLSs), thus providing a unifying framework based on a symmetry principle. All known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of GLSs (including topological terms and charges) and, most importantly, show the insufficiency of the energy spectrum, (recently defined) entanglement entropy, maximal string correlators, and fractionalization in establishing TQO. Duality mappings illustrate that not withstanding the existence of spectral gaps, thermal fluctuations can impose restrictions on suggested TQO computing schemes. Our results allow us to go beyond standard topological field theories and engineer new systems with TQO.