Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping.

We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy window around a critical energy, changes drastically. In the thin-torus limit, the entire spectrum is Anderson localized; however, an extensive number of states retain a Chern number C≠0. We resolve this apparent paradox by mapping the thin-torus quantum Hall system onto a disordered Thouless pump, where the Chern number corresponds to the winding number of an electron's path in real space during a pump cycle. We then characterize quantitatively the crossover between the one- and two-dimensional regimes for finite torus thickness, where the average Thouless conductance also shows anomalous scaling.

Fast Preparation of Critical Ground States Using Superluminal Fronts.

We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼L^{d} (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L^{2}) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids.

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.

Many-body localization in imperfectly isolated quantum systems.

We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that widely used diagnostics (such as many-body level statistics and expectation values in exact eigenstates) cease to show signatures of many-body localization above a critical coupling that is exponentially small in the size of the environment. However, we also identify alternative diagnostics for many-body localization, in the spectral functions of local operators. Diagnostics include a discrete spectrum and a hierarchy of energy gaps, including a universal gap at zero frequency. These alternative diagnostics are shown to be robust, and continue to show signatures of many-body localization as long as the coupling to the bath is weaker than the characteristic energy scales in the system. We also examine how these signatures disappear when the coupling to the environment becomes larger than the characteristic energy scales of the system.

Singular behavior of eigenstates in Anderson's model of localization.

We observe an apparent singularity in the electronic properties of the Anderson model of localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that occurs in dimensions d > 2. We present results of numerical calculations for Anderson's original uniform (box) distribution of on-site disorder in dimensions d = 1, 2, and 3. To establish this hitherto unreported behavior, and to understand its evolution with disorder, we contrast the behavior of two different measures of the localization length of the electronic wave functions-the averaged inverse participation ratio and the Lyapunov exponent. Our data suggest that Anderson's model exhibits richer behavior than has been established so far.

Realizing universal edge properties in graphene fractional quantum Hall liquids.

Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far has not been observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence of universality is the generic occurrence of edge reconstruction in such systems, which is the result of a competition between confinement potential and Coulomb repulsion. We show that due to a completely different mechanism of confinement, edge reconstruction can be avoided in graphene, which allows for the observation of the predicted universality.

Understanding and improving the Wang-Landau algorithm.

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, and identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation, and the statistical error is found to scale as square root of (ln f) with the modification factor f . This has implications for strategies for obtaining fast convergence.

The use of bisphosphonates in children: review of the literature and guidelines for dental management.

Bisphosphonates are inhibitors of osteoclastic bone resorption with therapeutic benefit in a variety of bone disorders in both adults and children. While these agents have been routinely used in adults for the past three decades, their more recent introduction into paediatric medicine means there is a paucity of data on long-term safety and effects on dental development. There is uncertainty regarding the dental management of children treated with bisphosphonates, particularly when invasive dental procedures, such as extractions and oral surgical procedures, are required. There are limited data with which to make recommendations about the dental management of patients treated with bisphosphonates, and there are no published recommendations that specifically address paediatric patients. This paper aims to outline paediatric uses and adverse effects of bisphosphonates and present recommendations on the dental management of children receiving bisphosphonates.

Effects of disorder on ferromagnetism in diluted magnetic semiconductors.

We present results of a numerical mean-field treatment of interacting spins and carriers in doped diluted magnetic semiconductors, which takes into account the positional disorder present in these alloy systems. Within our mean-field approximation, disorder enhances the ferromagnetic transition temperature for metallic densities not too far from the metal-insulator transition. Concurrently, the ferromagnetic phase is found to have very unusual temperature dependence of the magnetization as well as specific heat as a result of disorder. Unusual spin and charge transport is implied.

Interspecific associations among anophelines in different breeding habitats of Kheda district Gujarat: Part II--Non-canal area.

A total of 25,858 anophelines comprising 15 species emerged from 1104 samples of immatures from 9 breeding habitats surveyed for one year in six villages representing the non-canal area of Kheda district. Species diversity and homogeneity were maximum in seepage drains. An. annularis, An. barbirostris, An. culicifacies, An. stephensi and An. subpictus were ubiquitous. Interspecific associations occurred more commonly in habitats representing the stable ecosystem. Community groups of anophelines in different habitats were identified.

Disorder-driven collapse of the mobility gap and transition to an insulator in the fractional quantum Hall effect.

We study the nu=1/3 quantum Hall state in the presence of random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to distinguish unambiguously between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way and is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the mobility gap and plateau width narrow continuously and ultimately collapse, leading to an insulating phase.

Laterally modulated 2D electron system in the extreme quantum limit.

We report on magnetotransport of a two-dimensional electron system (2DES), located 32 nm below the surface, with a surface superlattice gate structure of periodicity 39 nm imposing a periodic modulation of its potential. For low Landau level fillings nu, the diagonal resistivity displays a rich pattern of fluctuations, even though the disorder dominates over the periodic modulation. Theoretical arguments based on the combined effects of the long-wavelength, strong disorder and the short-wavelength, weak periodic modulation present in the 2DES qualitatively explain the data.