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.