We perform calculations of the 3D finite-temperature homogeneous electron gas (HEG) in the warm-dense regime (rs ≡ (3/4πn) 1/3 a −1 B = 1.0−40.0 and Θ ≡ T /TF = 0.0625−8.0) using restricted path integral Monte Carlo (RPIMC). Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parameterized local density approximation (LDA) and our results around TF . These results can be used as a benchmark for improved functionals, as well as input for orbital-free DFT formulations. PACS numbers:The one-component plasma (OCP), a fundamental many body model, consists of a single species of charged particles immersed in a rigid neutralizing background. For electrons, the OCP is a model of simple metals and is often called the homogeneous electron gas (HEG), electron gas, or jellium. At zero-temperature, it is customary to define the natural length scale r s a B ≡ (3/4πn)and energy scale Ry = e 2 /2a B . When r s , the WignerSeitz radius, is small (high density) (r s → 0), the kinetic energy term dominates and the system becomes qualitatively similar to a non-interacting gas. At low density (r s → ∞), the potential energy dominates and the system is predicted to form a Wigner crystal [1]. In 3D at intermediate densities, a partially polarized state is predicted to emerge [2,3].Over the past few decades very accurate zerotemperature quantum Monte Carlo (QMC) calculations of the ground state HEG examined each of these phases [4,5]. In addition to determining phase boundaries, the results of these studies have proven invaluable in the rigorous parameterization of functionals in ground state density functional theory (DFT) [6].Recently there has been intense interest in extending the success of ground-state DFT to finite-temperature systems such as stellar, planetary interiors and other hot dense plasmas [7][8][9]. However, such attempts have met both fundamental and technical barriers when electrons have significant correlations.Some of the first Monte Carlo simulations explored the phases of the classical OCP [10]; note that its equation of state depends only on a single variable, the Coulomb coupling parameter Γ ≡ q 2 /(r s k B T ). First-order quantum mechanical effects have since been included [11,12]. However, the accuracy of these results quickly deteriorate as the temperature is lowered and quantum correlations play a greater role [13]. This breakdown is most apparent in the warm-dense regime where both Γ and the electron degeneracy parameter Θ ≡ T /T F are close to unity.Finite-temperature formulations of DFT have also met with challenges. There are two braod approaches to building finite-temperature functionals. In one approach, temperature effects are introduced by smearing the electronic density of states over a Fermi-Dirac distribution. As temperature increases, an ever-increasing number of molecular (Kohn-Sham) orbitals is required in order to evaluate the functional, making DFT calculations computationally intra...

Recent experiments claiming formation of quantum superposition states in near macroscopic systems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analysis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.

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Several properties of trapped hard sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single particle Gaussian and a hard sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard sphere radius and the number of particles. Special attention is given to diagonalizing the one body density matrix and obtaining the corresponding single particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital with highest occupation. The effect of interaction on other quantities such as the ground state energy, the mean radial displacement, and the momentum distribution are calculated as well. Results are compared with Mean Field theory in the dilute limit.

Effective methods for decoupling superconducting qubits (SQs) from parasitic environmental noise sources are critical for increasing their lifetime and phase fidelity. While considerable progress has been made in this area, the microscopic origin of noise remains largely unknown. In this work, first principles density functional theory calculations are employed to identify the microscopic origins of magnetic noise sources in SQs on an α-Al2O3 substrate. The results indicate that it is unlikely that the existence of intrinsic point defects and defect complexes in the substrate are responsible for low frequency noise in these systems. Rather, a comprehensive analysis of extrinsic defects shows that surface aluminum ions interacting with ambient molecules will form a bath of magnetic moments that can couple to the SQ paramagnetically. The microscopic origin of this magnetic noise source is discussed and strategies for ameliorating the effects of these magnetic defects are proposed.

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, na 3 < 10 −5 , where n = N/V and a is the hard core diameter, the condensate is localized at the center of the trap. As na 3 increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At na 3 ≤ 10 −4 the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At na 3 ≈ 10 −3 corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At na 3 > ∼ 10 −2 , mean field theory fails. At na 3 > ∼ 0.1, the Bosons behave more like a liquid 4 He droplet than a trapped Boson gas.

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (rs ≡ (3/4πn) 1/3 a −1 B < 40 and Θ ≡ T /TF > 0.0625). In doing so, we construct a Padé approximant which collapses to Debye-Hückel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

The phase diagram of Ca is examined using a combination of density-functional theory (DFT) and diffusion quantum Monte Carlo (DMC) calculations. Gibbs free energies of several competing structures are computed at pressures near 50 GPa. Existing disagreements for the stability of Ca both at low and room temperature are resolved with input from DMC. Furthermore, DMC calculations are performed on 0 K crystalline structures up to 150 GPa and it is demonstrated that the widely used generalized gradient approximation of DFT is insufficient to accurately account for the relative stability of the high-pressure phases of Ca. The results indicate that the theoretical phase diagram of Ca needs a revision.