Efficiency = Equity and Other Musings on Economics and Sustainable Development

Conventional wisdom says that equity concerns are beyond the scope of economic analysis and that achieving equity objectives will often come at a cost in terms of efficiency. Examination of the underlying meaning of efficiency and how it is defined, however, reveals that this tension between efficiency and equity is more apparent than real. The paper also explores the application of other economic concepts to the field of sustainable development, including the use of discounting for present value, Gross Domestic Product as a measure of well-being, and rational utility maximisation vs. bounded rationality as models of human behaviour.Agricultural and Food Policy, Community/Rural/Urban Development, Environmental Economics and Policy, Land Economics/Use, Research Methods/ Statistical Methods,

Emergent Chern-Simons excitations due to electron--phonon interaction

We address the problem of Dirac fermions interacting with longitudinal phonons. A gap in the spectrum of fermions leads to the emergence of the Chern--Simons excitations in the spectrum of phonons. We study the effect of those excitations on observable quantities: the phonon dispersion, the phonon spectral density, and the Hall conductivity.Comment: 9 pages, 4 figure

Short note on the density of states in 3D Weyl semimetals

The average density of states in a disordered three-dimensional Weyl system is discussed in the case of a continuous distribution of random scattering. Our result clearly indicate that the average density of states does not vanish, reflecting the absence of a critical point for a metal-insulator transition. This calculation supports recent suggestions of an avoided quantum critical point in the disordered three-dimensional Weyl semimetal. However, the effective density of states can be very small such that the saddle-approximation with a vanishing density of states might be valid for practical cases.Comment: 5 pages, 2 figures, minor changes, additional supplemen

Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene

The DC conductivity of monolayer and bilayer graphene is studied perturbatively for different types of disorder. In the case of monolayer, an exact cancellation of logarithmic divergences occurs for all disorder types. The total conductivity correction for a random vector potential is zero, while for a random scalar potential and a random gap it acquires finite corrections. We identify the diagrams which are responsible for these corrections and extrapolate the finite contributions to higher orders which gives us general expressions for the conductivity of weakly disordered monolayer graphene. In the case of bilayer graphene, a cancellation of all contributions for all types of disorder takes place. Thus, the minimal conductivity of bilayer graphene turns out to be very robust against disorder.Comment: 4 pages, 2 figures + supplementary material. Final version as published with PR

Renormalized transport properties of randomly gapped 2D Dirac fermions

We investigate the scaling properties of the recently acquired fermionic non--linear $\sigma$--model which controls gapless diffusive modes in a two--dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a novel renormalizable nonlocal field theory. For zero mean random gap, it is characterized by the absence of a dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.Comment: Version published with minor change

Conductivity of disordered 2d binodal Dirac electron gas: Effect of the internode scattering

We study the dc conductivity of a weakly disordered 2d Dirac electron gas with two bands and two spectral nodes, employing a field theoretical version of the Kubo--Greenwood conductivity formula. In this paper we are concerned with the question how the internode scattering affects the conductivity. We use and compare two established techniques for treating the disorder scattering: The perturbation theory, there ladder and maximally crossed diagrams are summed up, and the functional integral approach. Both turn out to be entirely equivalent. For a large number of random potential configurations we have found only two different conductivity scenarios. Both scenarios appear independently of whether the disorder does or does not create the internode scattering. In particular we do not confirm the conjecture that the internode scattering tends to Anderson localization

Two-parameter scaling theory of transport near a spectral node

We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-parameter scaling flow toward a finite fixed point. The latter is the minimal conductivity of the infinite system. Depending on boundary conditions, we also observe unstable fixed points with conductivities much larger than the experimentally observed values, which may account for results found in some numerical simulations. By including a spectral gap we extend our scaling approach to describe a metal-insulator transition.Comment: 4.5 pages, 4 figures, published versio