Linear Fluid Theory for Weakly Inhomogeneous Plasmas with Strong Correlations

Linearized fluid equations for the collective modes of weakly inhomogeneous plasmas including strong coupling effects are derived from a recent kinetic theory based on an extended Singwi‐Tosi‐Land‐Sjölander (STLS) ansatz [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90 , 011101(R) (2014)]. The equations are analogous to the equations of linearized elasticity theory with space dependent elastic moduli that correspond to those of a bulk system with the local fluid density. The identification of the latter as infinite‐frequency elastic moduli shows that the present version of the extended STLS theory accounts for the elastic properties of the fluid but does not capture the viscous behavior. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of finite-temperature local field corrections on many-body properties of quantum wires

The effect of low temperature on the many-body properties of an n-type GaAs-based quasi one-dimensional electron gas (quantum wire) has been investigated in the RPA, Hubbard and STLS approximations. Numerical results for the finite-temperature static structure factors, local field corrections, pair correlation functions, plasmon dispersion relations and inverse static dielectric functions of the system have been obtained and compared with the zero-temperature values. As a general result, the behavior of the system at finite-temperature does not change significantly at small values of wave vectors. Also, it has been found out that while applying the temperature dependent Hubbard and STLS to the quantum wire yields different results for local field corrections and pair correlation functions, the increase in temperature within all approximations causes the plasmon modes to shift upward in energy and the sharp peaks in the inverse static dielectric curve to become less pronounced.     

To the Theory of Inhomogeneous Electron Gas

Nonrigorous character of the density-functional theory for inhomogeneous electron gas based on the hypothesis assuming the existence of a universal density functional is demonstrated. A single-particle density matrix must be determined to calculate the ground-state energy of a finite system with a finite number of electrons. A single-particle Green function can be used to unambiguously determine the ground-state energy of an inhomogeneous electron system that satisfies the thermodynamic limit.     

Exact orbital-free kinetic energy functional for general many-electron systems

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.     

Nuclear energy density functionals constrained by low-energy QCD

A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional theory. Guided by two closely related features of QCD in the low-energy limit: a) in-medium changes of vacuum condensates, and b) spontaneous breaking of chiral symmetry; a relativistic energy density functional is developed and applied in studies of ground-state properties of spherical and deformed nuclei.     

Potential energy surfaces and lifetimes for spontaneous fission of heavy and superheavy elements from a variable density dependent mass formula

The potential energy surface for spontaneous fission is calculated using realistic density distributions for finite nuclei. Particular emphasis is placed on the region of the potential between the saddle and scission point. The method involves computing the energy of the system using an energy density functional consistent with varible density distributions and nuclear masses and obtained from a statistical many body theory. The results show that there exists an external or scission barrier to the fission process. Lifetimes and mass distributions which are computed using these potential energy surfaces are found to be in adequate agreement with observations for ²³⁴U, ²³⁶U, ²⁴⁰Pu, ²⁴⁴Cm, ²⁴⁸Cf, and ²⁵²Cf. Our predicted upper limit for the spontaneous fission half-lives of elements 112 and 114 is one year but the calculation indicates that these could be considerably shorter than a year.     

A Discrete Density Matrix Theory for Atoms¶in Strong Magnetic Fields

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B>> Z ^4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy. Received: 20 October 2000 / Accepted: 3 November 2000     

The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ‘Thomas Fermi’ (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone.     

The negative energy density for a three-single-electron state in the Dirac field

We examine the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime. We derive the conditions on which the energy density can be negative. We then show that the energy density satisfies two quantum inequalities in the ultrarelativistic limit.     

The Casimir effect for fermions in one dimension

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a “Dirac spike”) and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.     

Dependence of Tc on electronic density of states

From the Eliashberg gap equations generalized to include approximately an energy dependence in the electron density of states N(ε) we compute the functional derivative of the critical temperature T_c with N(ε). It is found to be a rapidly decreasing function of the increasing energy away from the Fermi energy. In an appropriate limit, a comparison with the predictions of the McMillan equation shows that it is inadequate in a study of δT_c/δN(ε).     

Thermodynamic limit for classical systems with Coulomb interactions in a constant external field

We introduce a new method for studying the thermodynamic limit for systems of particles with Coulomb interactions. The method is based on calculating the potential energy of the Coulomb interactions from the electric or magnetic fields in the system rather than from the energy of the individual particle — particle interactions. We are able to include the effects of a constant external field being imposed at the boundary of the system. The difficulties associated with Coulomb potentials being not even weakly tempered are overcome by imposing the boundary condition that at the boundary of the region containing the particles, the electric or magnetic field has normal component equal to that of the applied field. We prove that the thermodynamic free energy density exists and is independent of the sequence of regions used to define the limit. We introduce sequences of regions all of the same shape and show that for these sequences of regions the thermodynamic free energy density is independent of shape. Finally, we prove that the thermodynamic free energy is a convex function of the density of particles and of the applied field.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

HNO分子基态的结构与解析势能函数研究

应用群论及原子分子反应静力学的方法, 导出了HNO分子基态电子态和合理的离解极限.利用优选出的密度泛函理论B3LYP方法结合6-311G **优化计算了HNO分子基态的平衡结构和谐振频率.计算结果表明基态HNO分子稳定态为C_S构型,电子组态为X¹A',平衡核间距分别为R_H-N=0.1065 nm,R_N-O=0.1200 nm,键角∠H-N-O=108.60°,离解能D_e=15.379 eV.基态简正振动频率分别为:弯曲振动频率ν₁=1575.6351 cm^-1,对称伸缩振动频率ν₂=1673.2890 cm^-1,反对称伸缩振动频率ν₃=2837.7856 cm^-1.在此基础上,应用多体项展式理论导出了基态HNO分子的全空间解析势能函数,该势能函数等值势能图准确再现了HNO分子平衡结构和离解能. 关键词： 势能函数 光谱常数 密度泛函方法     

Density of states of random Schrödinger operators with a uniform magnetic field

We consider the density of states of Schrödinger operators with a uniform magnetic field and a random potential with a Gaussian distribution. We show that the restriction to the states of the first Landau level is equivalent to a scaling limit where one looks at the density of states near to the energy of the first Landau level and simultaneously lets the strength of the coupling to the random potential go to zero. We also consider a different limit where we look at the suitably normalised density of states near to the energy of the first Landau level when the intensity of the magnetic field goes to infinity.     

Central Limit Theorems for the Energy Density in?the?Sherrington-Kirkpatrick Model

In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein’s method in the quenched regime. The result for the energy density extends the corresponding result of Comets and Neveu in the case of zero external field.     

TiN分子基态(X2Σ)结构和势能函数

应用群论及原子分子反应静力学方法推导了TiN分子基态(X²Σ)的离解极限. 采用不同的密度泛函方法,包括BP86, B3P86, B3LYP, B3PW91, 分别选用不同的基组对TiN分子基态进行结构优化计算.通过比较得出使用BP86方法, 对N原子使用D95V++(d,P)基组和Ti原子使用6-311++G^**基组时,计算得到的平衡几何结构、分子离解能和谐振频率与实验值符合得最好. 并采用最小二乘法拟合改进的Murrell-Sorbie函数得到了相应电子态的完整势能函数. 计算得到的光谱常数与实验光谱数据符合得很好. 关键词： BP86 TiN分子基态 势能函数 光谱常数