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.     

On the thermodynamicV-representability of one-particle density matrices

We consider thermodynamicallyV-representable one-matrices, i. e., one-particle density matrices that are obtained by reducing the Gibbs grand canonical density matrix of a quantum mechanical many-particle system subject to a suitable external potential, and show them to obey an inequality lower bounding their eigenvalues in terms of those of the one-particle kinetic energy operator. The result imposes a severe constraint on the asymptotic behavior of the eigenvalues of any one-matrix to beV-representable. For noninteracting particles, the corresponding upper bound is also proven, implying that a one-matrix can be interactionlesslyV-representable for at most one temperature. We expect the upper bound to be valid more generally, as is illustrated by a model of coupled harmonic oscillators where theV-representable one-matrices can be explicitly calculated, and discuss its implications for certain aspects of density-matrix functional theory.     

Shell-model hamiltonians with generalized seniority eigenstates

The conditions on shell-model Hamiltonians which have eigenstates with generalized seniority 1) v = 0 and v = 2 are stated and investigated in detail. For even semi-magic nuclei the conditions for v = 0 eigenstates give rise to a simple binding-energy formula with terms linear and quadratic in nucleon number. If the v = 2 conditions are also satisfied, constant spacings independent of nucleon number are obtained between ground states and the low-lying J = 2, 4, …, levels. This feature is clearly demonstrated by the existence of a single-particle operator which transforms the v = 0 state into one with v = 2 and which obeys a linear equation of motion when acting on the v = 0 state. The constant spacings are obtained in the general case for one state with a given J, unlike the situation in the quasi-spin scheme in which there are n-independent separations between all levels. Examples are given of cases in which these conditions are actually fulfilled and yet in which the eigenstates are not those of the quasi-spin formalism.     

Cellular theory of ordered AB alloys

The heat and volume of formation of ordered simple metal AB alloys are calculated using the density functional formalism. A new method is proposed in which the alloy is partitioned into cells defined by surfaces on which the gradient of the electron density vanishes. The total alloy energy is formulated in terms of cellular and Madelung contributions and is minimized subject to the constraint of equal A and B cell boundary densities. Quantitative results for LiMg are presented.     

Analysis of the transport coefficients for simple dense fluids: The diffusion and bulk viscosity coefficients

The analysis of transport coefficients based on the modified Enskog theory (MET), discussed in a previous publication, has been extended to include the self-diffusion coefficient (D) and the bulk viscosity coefficient (η_v). Specifically, calculated values according to the MET are compared with experiment over the range for which data are available. Fluids considered are argon, nitrogen and methane. Agreement between theory and experiment for densities less than about twice the critical density (ρ_c) is generally within about 10%. However, much of the data was taken at densities well in excess of 2_ρc in which case agreement is still not unsatisfactory. Deviations exceeding 10% between theoretical and experimental self-diffusion coefficients were observed for densities in the approximate range 0.9 ? _ρ/ρc ? 2.0. It is possible that these deviations are due to long range correlated molecular motions which are not present in the MET. The sound absorption is also briefly considered. Finally, the behavior of η_v and D at low densities is discussed.     

Searching for new conditions for fermion N-representability

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N = 3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction.     

Schrödinger picture formalism of Φ6 theory

The static effective potential for a scalar field with Φ⁶ interaction is calculated using the effective action in Schrödinger picture formalism. It is found that the effective potential obtained is same as the Gaussian effective potential as far as static case is concerned. Equivalence with the CJT formalism can also be established. As in CJT formalism after renormalization an unrenormalized mass term persists. Nonzero turning points are obtained both for positive and negativeλ. Results are analysed numerically. Graphical analysis indicates a behaviour similar to that obtained for CJT formalism at zero temperature.     

Spectroscopy of XY2Z2 (C2v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃Td⊃C2v Chain. Application to the Ground State of SO2F2

A tensorial formalism adapted to the case of quasi-spherical XY₂Z₂ asymmetric tops such as SO₂F₂ has been developed as an extension of the usual one for the tetrahedral molecules. We use the O(3)⊃T_d⊃C_2v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C_2v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for these operators. A first application to the ground state of SO₂F₂ is presented. Programs for spectrum simulation and fit using these methods are freely available at the URL http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential

In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N ? 1 electrons. The optimal effective charge density (electron repulsion density, ρ_rep) and the corresponding optimal effective potential (electron repulsion potential v_rep) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from v_rep, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39% and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.     

Spectroscopy of XY3Z (C3v) molecules: A tensorial formalism adapted to the O (3) ⊃ C∞v ⊃ C3v group chain

A tensorial formalism adapted to the case of XY₃Z symmetric tops has been developed. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. All the coupling coefficients and formulas for the computation of the matrix elements are given for this chain. Such relations are also deduced in C_3v group itself.     

Saturation and condensate fraction reduction of cold alpha matter

The ground state energy of ideal α  -matter at T=0$T=0$ is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α–α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande–Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction.     

Electronic properties and Compton profiles of molybdenum dichalcogenides

We present the first ever experimental Compton profiles of molybdenum dichalcogenides (MoX₂; X=S and Te) using 20 Ci ¹³⁷Cs Compton spectrometer. To interpret our experimental data, we have computed the theoretical profiles, energy bands and density of states using linear combination of atomic orbitals method in the framework of density functional theory and its hybridisation with Hartree Fock. The energy bands and density of states using full potential linearised augmented plane wave method have also been computed. Both theories show the existence of the indirect band gap. In addition, the relative nature of bonding is explained in terms of equal-valence-electron-density profiles and valence band charge densities.     

On the study of the vibrational energy levels of Arsine molecule

We compare two formalisms applied to the vibrational modes of the molecule of AsH₃ of C_3v molecular symmetry group. Indeed, the close stretching modes of this molecule may be considered as those of a three-dimensional oscillator whereas the bending modes may be considered either as a one-dimensional oscillator of symmetry A₁ and a two-dimensional oscillator of symmetry E or as an approximate three-dimensional oscillator. So, we have applied the U(p + 1) formalism to the both stretching and bending modes and introduced coupling terms acting on an appropriate coupled vibrational basis through a local mode formalism. We have then compared the result of our fitting with those obtained with the coupling of a local mode formalism adapted to the stretching vibrations with a normal mode formalism for the bending ones. Finally we compare our results with other methods recently proposed in the literature.     

Nonequilibrium second-order phase transitions in stochastic lattice systems: A finite-size scaling analysis in two dimensions

Two-dimensional lattice-gas models with attractive interactions and particleconserving happing dynamics under the influence of a very large external electric field along a principal axis are studied in the case of a critical density. A finite-size scaling analysis allows the evaluation of critical indexes for the infinite system asβ=0.230±0.003,v=0.55±0.2, and α 0. We also describe some qualitative features of the system evolution and the existence of certain anisotropic order even well above the critical temperature in the case of finite lattices.     

The ground state rotational spectrum of SO2F2

The analysis of the ground state rotational spectrum of SO₂F₂ [K. Sarka, J. Demaison, L. Margulès, I. Merke, N. Heineking, H. Bürger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55] has been performed with the Watson’s Hamiltonian up to sextic terms but shows some limits due to the A and S reductions. Since SO₂F₂ is a quasi-spherical top, it can also be regarded as derived from an hypothetical XY₄ molecule. Thus we have developed a new tensorial formalism in the O(3)⊃T_d⊃C_2v group chain (M. Rotger, V. Boudon, M. Loëte, J. Mol. Spectrosc. 216 (2002) 297]. We test it on the ground state of this molecule using the same experimental data (10 GHz-1 THz region, J up to 99). Both fits are comparable even if the formalisms are slightly different. This paper intends to establish a link between the classical approach and the tensorial formalism. In particular, our tensorial parameters at a given order of the development are related to the usual ones. Programs for spectrum simulation and fit using these methods are named C_2vTDS. They are freely available at the URL:http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B∧F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci–Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.     

Spin density functional formalism for surface susceptibility of a nearly ferromagnetic metal

Within the density functional formalism the surface spin susceptibility of a nearly ferromagnetic metal is examined for the case of an exchange interaction with finite range and varying with the distance from the surface. It is found that a ferromagnetic instability at the surface exists for a range r_c < 1/1.4k_f.     

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.