Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Theorems on n-representability in finite dimensions

The subject of the paper is the n-representability problem of p-particle density operators, and, in general, of p-particle positive operators in the case when the 1-particle reference space is of finite dimension r.     

Transition probabilities and static moments of excited states in even-even nuclei

A new approach is made to calculate the generalized single-particle density matrixp ^μv in even-even nuclei. It is shown that this quantity is included in the three particle response function, for which we derived a renormalized equation. Taking into account in a consequent way the effective particle-hole interaction we received a formula for the static moment of excited states and the transition probability between such states which is essentially different from the usual RPA theory.     

Exact local in time evolution equations for macroobservables

By introducing an evolution equation for the generalized Gibbs state σ(t), the N-particle distribution function is expressed as a linear functional of σ(t). Exact equations local in time for the time evolution of macroobservables are obtained. The kinetic coefficients appear as the fixed point of a conveniently defined microscopic expression which may be considered as a natural extension of the Kubo formula.     

A new mass measurement of29Mg. Observation of excited states via the13C(18O,2p)29Mg reaction

A direct measurement of the mass of the neutron rich nucleus²⁹Mg has been performed via the¹³C(¹⁸O,2p)²⁹Mg reaction. Excitation energies in²⁹Mg are also deduced from the 2p-particle spectra, and compared with theory.     

On the Q-condition for fermion N-representability

It is shown that if a 2-particle fermion density operator satisfies the Q-condition for N-representability, then its 1-particle contraction is N-representable. This is an extension of Coleman's theorem to the infinite rank case.     

Some necessary conditions for fermion N-representability

The analogues of the Q and B conditions for the N-representability of a p-particle fermion density operator are derived. These conditions impose some new necessary conditions for the N-representability of 2-density operators. It is shown that the new conditions are no more restrictive than the conventional Q and B conditions.     

s- and p-wave neutron spectroscopy. Xe. Intermediate structure in 90Y and the generalized R-matrix theory

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross section measurements in the range of 0.3 to 1.2 MeV incident energy was investigated using the generalized R-matrix theory of nuclear reactions and the doorway interpretation of intermediate structure. The energies and wave functions of the doorway resonances were calculated in a 2-particle and 3p-1h basis of the shell model. The model space and the parameters of the model calculation chosen were consistent with other shell model calculations in the mass-90 region. Several strong p-wave doorways with J^π = 0⁺, 1⁺, and 2⁺ were predicted by the model in the energy range studied. This is due to proximity of p-wave giant resonance. The escape widths Γ^↑ and the spreading widths Γ^↓ for these states were evaluated using the model wave functions and the R-matrix formalism. The calculated energy dependence of the total cross section shows that most of the predicted doorways are in general agreement with the observed anamolies with similar relative strength. More significantly, the underlying p-wave gross structure representing a grand average is of very similar shape in both theory and experiment. As expected in the mass 90-region, the s- and d-wave doorways contribute less significantly to the calculated resonance structure.     

Hydrogen storage: Lattice dynamics of orthorhombic NaMgH3

In this work, we investigate the structural, dynamic and thermodynamic properties of NaMgH₃, devoted for hydrogen storage. Density functional theory using pseudopotential methods and generalized gradient approximation has been used. A good agreement between the calculated structural parameters and the experimental data was found. A linear-response approach for the density functional theory is used in order to derive the Born effective charge tensors, the dielectric permittivity tensors, the phonon frequencies at the center of the Brillouin zone, the phonon-dispersion curves and the corresponding density of states for NaMgH₃ material. The obtained phonon frequencies at the zone center (Γ point) for the Raman-active and infrared-active modes are analyzed. Thermodynamic functions using the phonon density of states are also calculated.     

First-principles study on the electronic and magnetic properties of InN nanosheets doped with 2p elements

The electronic structure of InN nanosheets doped by light elements (Be, B, C, and O) is studied based on spin-polarized density functional theory within the generalized gradient approximation. The results show that the Be and C dopants in InN nanosheets induce spin polarized states in the band gap, or near the valence band, which generates local magnetic moments of 1.0 µ_B with one dopant atom. Due to the exchange spin-splitting, the three 2p electrons of Be atom are all in p_x and p_y orbitals (↑↑↓). So Be will coordinate with host atoms by σ coordination bond. The long-range ferromagnetic order above room temperature is attributed to p–p coupling. For C atom, the configuration of the five 2p electrons is (↑↑↑↓↓), and the unpaired electron is in p_z(↑) orbital. So the π bond will be formed between C atom and other atoms. Due the weak π bond cannot support long-range coupling, no stable magnetism is sustained if two C dopants are separated by longer than 3.58 Å.     

Optical properties of SiC nanocages: ab initio study

The structural, electronic and optical properties of Si _n C _n (n=12,16,20,30,35 and 60) nanocages were studied using different approximations of density functional theory, i.e. local density approximation (LDA), generalized gradient approximation (GGA) and density functional theory based tight binding approximation (DFTB). The highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) energy gaps were calculated for all nanocages. Time-dependent density functional theory (TD-DFT) was also applied for estimating of the optical excitation and exciton binding energies of the nanocages and the results compared with pure DFT calculations.     

A generalized Hartree-Fock-Bogoliubov approach for the description of band structures in nuclei: (I). Formulation of the theory and its exact solution in the framework of the SU(3) model

The SU(3) model is studied in the framework of the generalized Hartree-Fock-Bogoliubov approach, proposed in the papers of Kerman and Klein, and Beliaev and Zelevinski. In this model the mentioned approach is equivalent to the exact solution of the problem. The generalized density matrix R defined in the product space of single-particle and nuclear states is calculated analytically. Its eigenvalues, the occupation numbers in the average field, differ essentially from one. Thus the normalization condition $\text{R}{}^2\text{=}\text{R}$ used in the HFB theory is not valid in the generalized approach.     

Density functional calculation of Compton profiles of metals using phase-space approach

Spherically averaged electron momentum densities (EMD) in Al, V and Cu metals have been calculated by using density functional theory in the phase-space approach. Compton profiles, J(q) and expectation values 〈pⁿ〉 have been computed. These theoretical results show satisfactory agreement with the experimental data for Al, V and Cu.     

Quantum Dynamics with Mean Field Interactions: a New Approach

We propose a new approach for the study of the time evolution of a factorized N-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the N-particle Schrödinger equation is shown to converge to the projection onto the one-dimensional subspace spanned by the solution to the Hartree equation with a speed of convergence of order 1/N for all fixed times.     

A scaling theory of clusters in the lattice gas

It is proposed that the number ofp-particle,k-bond lattice gas cluster configurations is of the form exp{σpf(k/p)} in the limitp→t8. A simple modification permits application to finite clusters, with the consequence that asymptotically the cluster partition function is of the droplet form, i.e., Z _p =exp[kp{itμp^1?1/d }+O(ln p)]. The scaling function for two-dimensional lattices is determined numerically and is found to be qualitatively universal. The scaling theory is used to investigate the size dependence of the surface free energy. The surface tension of small clusters can significantly exceed its limiting value. For intermediate cluster sizes (～100 particles) there is a modest reduction in surface tension, in accord with Tolman's prediction and the results of recent Monte Carlo studies.     

Structural, electronic, elastic and optical properties of fluoro-perovskite KZnF3

We determine the structural, electronic, elastic and optical properties of fluoro-perovskite KZnF₃ using the full potential linear augmented plane wave approach (FP-LAPW) based on the density functional theory (DFT). The exchange-correlation potential is treated by the local density approximation (LDA) and the generalized gradient approximation (GGA). The calculated structural parameters are in good agreement with the available data. We have obtained an indirect band gap. The effect of the pressure on the band gaps is investigated. We evaluate the elastic constants (C_ij), elastic moduli and the Debye temperature. The imaginary and the real parts of the dielectric function ε(ω) and some optical constants are also calculated.     

Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

The quantal system of Bose particles described by the non-linear Schrödinger equation i?φ/?t = -$\text{1}\text{2}$?²φ/?x² + cφ1φ², with c= cxf∞ and via the ground state with finite particle density, is the 1- dimensional gas of impenetrable bosons studied by M. Girardeau, T.D. Schultz, A. Lenard, H.G. Vaidya and C.A. Tracy. We show that the 2-point (resp. 2n-point) function, or the 1-particle (resp. n-particle) reduced density matrix, of this system satisfies a non-linear differential equation (resp. a system of non-linear partial differential equations) of Painlevé type. Derivation of these equations is based on the link between field operators in a Clifford group and monodromy preserving deformation theory, which was previously established and applied to the 2-dimensional Ising model and other problems. Several related topics are also discussed.     

Ferromagnetic origin of Na and Mn codoped CaZn<Subscript>2</Subscript>As<Subscript>2</Subscript> diluted magnetic semiconductor: A first-principles study

We have investigated the electronic structure and magnetic properties of Na and Mn codoped CaZn₂As₂ using density functional theory within the generalized gradient approximation (GGA)+U schemes. We have shown that the ground state magnetic structure of Mn-doped CaZn₂As₂ is antiferromagnetic while holemediated Zener’s p–d exchange is responsible for the origin of ferromagnetism of Na and Mn codoped CaZn₂As₂.     

Aluminum Hugoniot from model calculations including semicore electrons based on density functional theory

We present a method to obtain Hugoniot from model calculations based on density functional theory, and apply the method to aluminum Hugoniot. Technological advances have extended the experimental research of high energy density physics, and call for quantitative theoretical analysis. However, direct computation of Hugoniot from density functional theory is very difficult. We propose two step calculations of Hugoniot from density functional theory. The first step is molecular dynamics simulations with an ambient temperature for electrons. The second step is total energy calculations of a crystal with desired high temperatures for electrons and with the ambient temperature for electrons. We treated the semicore 2s and 2p electrons of aluminum as valence electrons only for the total energy calculations of the aluminum crystal. The aluminum Hugoniot from our model calculations is in excellent agreement with available experimental data and the previous density functional theory calculations in the literature.     

Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics

In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The Lagrangian density of the gauge field depends on the curvature of the connection which can be calculated from the holonomy around (infinitesimal) loops. For Abelian symmetry groups, say G=U(1), there exists a generalization, known as p-form electrodynamics, in which (p−1)-dimensional charged objects can be propagated along p-surfaces and in which the Lagrangian depends on a generalized curvature associated with (infinitesimal) closed p-surfaces. In this article, we use Lie 2-groups and ideas from higher category theory in order to formulate a discrete gauge theory which generalizes these models at the level p=2 to possibly non-Abelian symmetry groups. An important feature of our model is that it involves both parallel transports along paths and generalized transports along surfaces with a non-trivial interplay of these two types of variables. Our main result is the geometric picture, namely the assignment of non-Abelian quantities to geometrical objects in a coordinate free way. We construct the precise assignment of variables to the curves and surfaces, the generalized local symmetries and gauge invariant actions and we clarify which structures can be non-Abelian and which others are always Abelian. A discrete version of connections on non-Abelian gerbes is a special case of our construction. Even though the motivation sketched so far suggests applications mainly in string theory, the model presented here is also related to spin foam models of quantum gravity and may in addition provide some insight into the role of centre monopoles and vortices in lattice QCD.