Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas.

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10^{124} matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration path-integral formalism disagree by up to ∼10% at certain reduced temperatures T/T_{F}≤0.5 and densities r_{s}≤1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T/T_{F}≥1 and r_{s}≤2.

Single-electron induced surface plasmons on a topological nanoparticle.

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators-materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. For topological insulators, the effects of these surface states will be more strongly pronounced in the case of nanoparticles. Here we show that under the influence of light a single electron in a topologically protected surface state creates a surface charge density similar to a plasmon in a metallic nanoparticle. Such an electron can act as a screening layer, which suppresses absorption inside the particle. In addition, it can couple phonons and light, giving rise to a previously unreported topological particle polariton mode. These effects may be useful in the areas of plasmonics, cavity electrodynamics and quantum information.

Interaction picture density matrix quantum Monte Carlo.

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

Dynamics of thermalization and decoherence of a nanoscale system.

We study the decoherence and thermalization dynamics of a nanoscale system coupled nonperturbatively to a fully quantum-mechanical bath. The system is prepared out of equilibrium in a pure state of the complete system. We propose a random matrix model and show analytically that there are two robust temporal regimes in the approach of the system to equilibrium-an initial Gaussian decay followed by an exponential tail, consistent with numerical results on small interacting lattices [S. Genway, A. F. Ho, and D. K. K. Lee, Phys. Rev. Lett. 105, 260402 (2010)]. Furthermore, the system decays towards a Gibbs ensemble in accordance with the eigenstate thermalization hypothesis.

A K-nearest neighbors survival probability prediction method.

We introduce a nonparametric survival prediction method for right-censored data. The method generates a survival curve prediction by constructing a (weighted) Kaplan-Meier estimator using the outcomes of the K most similar training observations. Each observation has an associated set of covariates, and a metric on the covariate space is used to measure similarity between observations. We apply our method to a kidney transplantation data set to generate patient-specific distributions of graft survival and to a simulated data set in which the proportional hazards assumption is explicitly violated. We compare the performance of our method with the standard Cox model and the random survival forests method.

Critical supercurrents and self-organization in quantum Hall bilayers.

We present a theory of interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. In agreement with recent experiments [Phys. Rev. B 80, 165120 (2009); Phys. Rev. B 78, 075302 (2008)], we find that the critical current is proportional to the sample area and is comparable in magnitude to observed values. This reflects the formation of a Bean critical state as a result of current injection at the boundary. We predict a crossover to a critical current proportional to the square-root of the area in smaller samples. We also predict a peak in the critical current as the electron density varies at fixed layer separation.

Dynamics of thermalization in small Hubbard-model systems.

We study numerically the thermalization and temporal evolution of a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum degeneracy, the subsystem can reach a steady state resembling equilibrium. This occurs for a nonperturbative coupling between the subsystem and the rest of the lattice where relaxation to equilibrium is Gaussian in time, in sharp contrast to perturbative results. We find similar results for random couplings, suggesting such behavior is generic for small systems.

Spin textures, screening, and excitations in dirty quantum Hall ferromagnets.

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential. Describing these systems with a classical nonlinear sigma model and using analytical estimates supported by results from numerical simulations, we examine the nature of the ground state as a function of disorder strength, Delta, and deviation, deltanu, of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration, and in the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at small Delta and /deltanu/ to a spin glass at larger Delta or /deltanu/. We examine ground-state response functions and excitations.