Momentum distribution of the homogeneous electron gas

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)?10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.     

Spin-resolved correlations in the warm-dense homogeneous electron gas

We have studied spin-resolved correlations in the warm-dense homogeneous electron gas by determining the linear density and spin-density response functions, within the dynamical self-consistent mean-field theory of Singwi et al. The calculated spin-resolved pair-correlation function g _{σ σ′}(r) is compared with the recent restricted path-integral Monte Carlo (RPIMC) simulations due to Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)], while interaction energy E _int and exchange-correlation free energy F _xc with the RPIMC and very recent ab initio quantum Monte Carlo (QMC) simulations by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. g _↑↓(r) is found to be in good agreement with the RPIMC data, while a mismatch is seen in g _↑↑(r) at small r where it becomes somewhat negative. As an interesting result, it is deduced that a non-monotonic T-dependence of g(0) is driven primarily by g _↑↓(0). Our results of E _int and F _xc exhibit an excellent agreement with the QMC study due to Dornheim et al., which deals with the finite-size correction quite accurately. We observe, however, a visible deviation of E _int from the RPIMC data for high densities (~8% at r _s = 1). Further, we have extended our study to the fully spin-polarized phase. Again, with the exception of high density region, we find a good agreement of E _int with the RPIMC data. This points to the need of settling the problem of finite-size correction in the spin-polarized phase also. Interestingly, we also find that the thermal effects tend to oppose spatial localization as well as spin polarization of electrons.     

Calculation of the nonlinear susceptibilities of interacting homogeneous electron gas by the density functional method

The density functional method is used for the calculation of nonlinear susceptibilities of an interacting electron gas. It is shown that this approach leads to the expression for nonlinear susceptibilities which satisfy exactly the strict sum rules derived previously. By using the local densities approximation we obtain the expression for the exchange-correlation contribution in the first non-linear susceptibility of interacting electron gas. It is shown that such a contribution may have a noticeable effect on the binding energy and phonon spectrum of polivalent simple metals.     

Origin of the electron spin resonance signal in the manganites: from polarons to phase separation

In the manganites L_1?xM_xMnO₃ (L = La, Nd, Pr, …; M = Sr, Ba, Ca, …), the doping concentration introduces a mixed valence (Mn³⁺, Mn⁴⁺) which governs the magnetic and electric properties of the compound. Mn³⁺ (S = 2) is scarcely observed in electron spin resonance (ESR). In contrast, Mn⁴⁺ (S = 3/2), is a good ESR probe. However, X-band measurements show an enhanced Mn⁴⁺ susceptibility, which is the signature of some kind of coupling of the Mn⁴⁺ ions with the Mn³⁺ ions, but its exact nature is still controversial. We present multifrequency ESR experiments (9–385 GHz) obtained on different systems (La_1?δMnO₃, La_1?xMnO₃, La_1?xCa_xMnO₃, and Nd_1?xCa_xMnO₃) in the low-concentration range (0 <x< 0.33). In the paramagnetic regime, the Mn³⁺ spectrum cannot be observed because of fast relaxation. The signal arises from polarons, whose size, temperature and magnetic field dependences vary with M andx. The single line observed in the metallic compound evolves towards a double-peak structure visible at high frequency in La_0.97MnO₃. Its evolution with temperature below the magnetic transition reveals the presence of manganese ions in a different magnetic environment, i.e., phase separation. The magnetic order of the separated phase is not ferromagnetic. It is a more complex order, which depends substantially on the nature of the cation M.     

Dynamical stability of infinite homogeneous self-gravitating systems and plasmas: application of the Nyquist method

We evolve an effective interatomic interaction potential with long range Coulomb interactions, Hafemeister and Flygare type short range overlap repulsion extended up to second neighbor ions and van der Waals interaction to discuss the pressure dependent first order phase transition, mechanical, elastic, and thermodynamical properties of NaCl-type (B1) to CsCl-type (B2) structure in lanthanum pnictides (LaY, Y = N, P, As, Sb, and Bi). Both charge transfer interactions and covalency effect apart from long range Coulomb are important in revealing the high-pressure structural phase transition, associated volume collapse, elastic and thermodynamical properties. By analyzing the aggregate elastic constants pressure (temperature) dependence, the rare earth lanthanum pnictides are mechanically stiffened as a consequence of bond compression and bond strengthening attributed to mechanical work hardening, thermally softening arose due to bond expansion and bond weakening due to lattice vibrations, brittle (ductile) nature at zero (increased) pressure and temperature dependent brittleness from room temperature to high temperatures. To our knowledge these are the first quantitative theoretical prediction of the pressure and temperature dependence of elastic and thermodynamical properties explicitly the mechanical stiffening, thermally softening, and brittle (ductile) nature of rare earth LaY (Y = N, P, As, Sb and Bi) pnictides and still awaits experimental confirmations.     

Hybrid functionals and GW approximation in the FLAPW method

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.     

An eigenvalue method to study the threshold behaviors of plasmonic nano-lasers

An eigenvalue method is proposed to study the threshold behaviors of plasmonic nano-lasers. The medium gain and dispersion are taken into consideration based on semi-classical laser dynamics, and therefore the lasing threshold, mode pattern, and lasing frequency can be theoretically predicted. The lasing properties of dielectric, plasmonic core, and plasmonic shell nano-lasers are investigated in details. It is found that the lasing thresholds of nano-lasers can be reduced by two orders of magnitude when introducing localized surface plasmon modes.     

The influences of gas and electron temperatures on electron attachment in gas electrical discharges

Various electron attachment processes are reviewed, emphasising the way in which the rates and products of some selected reactions vary with the attaching gas temperatureT _g, the temperature,T _e, and the energy of the attaching electrons. The examples illustrating the variety of reactions are the efficient dissociative attachment reaction to CCl₄, attachment to SF₆ which involves both dissociative and non-dissociative attachment, attachment to CHCl₃ which requires activation energy, and attachment to CCl₃Br which results in both Cl- and Br- product ions. A model has been presented which is able to quantitatively explain the difference influences ofT _g andT _e on the rates of some of these reactions. Also described are the unusually efficient attachment properties of the fullerene molecules C₆₀ and C₇₀ as revealed by our FALP experiments, noting that these molecules have potential importance as efficient suppressers of electrical breakdown through gases such as those used to insulate high voltage devices. We emphasise throughout this paper the importance of an understanding of the separate influences of gas and electron temperature on attachment reactions for the modelling of practical gas discharge media such as etchant plasmas. We dedicate this paper to Professor Jan Janča on the occasion of his sixtieth birthday in recognition of his major contributions to gas discharge physics.     

The homogeneous Boltzmann hierarchy and statistical solutions to the homogeneous Boltzmann equation

An existence and uniqueness result for the homogeneous Boltzmann hierarchy is proven, by exploiting the statistical solutions to the homogeneous Boltzmann equation.     

Quantum corrections to the energy density of a homogeneous Bose gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of , where is the number density and a is the S-wave scattering length. We calculate the ground state energy density to second order in . The coefficient of the correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on a, but also on an extra parameter that describes the low energy scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is ,and is the length scale set by the van der Waals potential. Received 2 February 1999     

The electron gas: inclusion of antiparallel spin correlations

An electron gas with a uniform neutralizing background is the canonical model for the study of the properties of an interacting many-body system. Most treatments of this problem treat inadequately the correlations between anti-parallel spins which are expected to influence strongly certain properties of the system. Using a new variational formulation, we show how to handle the non-linearities introduced into the many-body equations by such correlations; the compressibility is lowered and the paramagnetic susceptibility enhanced.     

Two examples of non-radiative systems—An application of homogeneous functions to Synge's approximation method

A method of finding approximations for the gravitational field of two non-radiative systems is given. The first system consists of a shrinking body with convex boundary, having certain symmetries. The second system consists of two shrinking bodies which, in the first approximation, approach each other along thex ₁-axis with a certain constant relative velocity. The two bodies are assumed to have rotational symmetry around thex ₁-axis.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.Supported by N.R.C. Grant No. A-5205.     

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.     

GW170817: The key to the door of multi-messenger astronomy including gravitational waves

正On September 14,2015,the Laser Interferometer Gravitational-wave Observatory(LIGO)team achieved the first-ever direct detection of a gravitational wave(GW)event from a binary black hole(BH)merger(GW150914),indicating the opening of GW observational window[1].The success of LIGO is due to the tremendous developments in experimental technologies[2-6].As of October 2017,the LIGO(later joint by VIRGO)team had published 3 additional BHBH merger events(GW151226,GW170104,GW170814)     

Effects of confinement on a magnetized ideal gas: I. The electron gas

Using the framework of the grand canonical ensemble the effects of a two (or three) dimensional confinement (harmonic) potential on the magnetic properties of an ideal electron gas are investigated. The high temperature results for the magnetic moment obtained by Felderhof and Raval are generalized to take into account the spin. At low temperature the confinement potential introduces a new oscillatory phenomena besides a modification or even a destruction of the de Haas-van Alphen effect. The changes in Landau diamagnetism are also analysed.