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.     

Two necessary conditions for fermion N-representability

Two necessary conditions for N-representability of fermion 2-matrices are studied. Each determines a convex set which contains the set of N-representable 2-matrices. The mutual relations of these three sets are discussed. When the rank of the fermion system is less than or equal to N+2 these conditions are necessary and sufficient. A variation procedure, involving only D², is given for obtaining upper and lower bounds on the lowest eigenvalue of any two-particle observable.     

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.     

The structure of the Q-family of mappings in the n-representability theory II

The extreme and non-trivial elements of the convex hull of the Q-like mappings, derived in part I, are determined and the associated family of n-representability conditions for p-density operators is reduced to an equivalent set of p independent conditions.     

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

We propose the P_N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P_N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.     

Photophysical characteristics of three novel benzanthrone derivatives: Experimental and theoretical estimation of dipole moments

The effect of solvents on absorption and fluorescence spectra and dipole moments of novel benzanthrone derivatives such as 3-N-(N′,N′-Dimethylformamidino) benzanthrone (1), 3-N-(N′,N′-Diethylacetamidino) benzanthrone (2) and 3-morpholinobenzanthrone (3) have been studied in various solvents. The fluorescence lifetime of the dyes (1-3) in chloroform were also recorded. Bathochromic shift observed in the absorption and fluorescence spectra of these molecules with increasing solvent polarity indicates that the transitions involved are π→π^?. Using the theory of solvatochromism, the difference in the excited-state (μ_e) and the ground-state (μ_e) dipole moments was estimated from Lippert-Mataga, Bakhshiev, Kawski-Chamma-Viallet, and McRae equations by using the variation of Stokes shift with the solvent’s relative permittivity and refractive index. AM1 and PM6 semiempirical molecular calculations using MOPAC and ab-initio calculations at B3LYP/6-31 G^? level of theory using Gaussian 03 software were carried out to estimate the ground-state dipole moments and some other physicochemical properties. Further, the change in dipole moment value (Δμ) was also calculated by using the variation of Stokes shift with the molecular-microscopic empirical solvent polarity parameter (E_T^N). The excited-state dipole moments observed are larger than their ground-state counterparts, indicating a substantial redistribution of the π-electron densities in a more polar excited state for all the systems investigated.     

Fourier transform microwave spectroscopy of N,N-dimethylacetamide

The jet-cooled Fourier-transform microwave spectrum of N,N-dimethylacetamide was recorded in the region of 12-24 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Coriolis-like coupling parameters characterizing interaction between internal rotation of methyl groups and the overall rotation were also determined from internal-rotation tunneling splittings of the rotational transitions. The Coriolis-like coupling parameters permitted determination of the barrier heights to internal rotation of the three methyl groups, which were found to be 677, 237, and 183 cm⁻¹ for the C-methyl top, the trans-N-methyl top and the cis-N-methyl top, respectively.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Spectroscopic and theoretical evidence for the photoinduced twisted intramolecular charge transfer state formation in N,N-dimethylaminonaphthyl-(acrylo)-nitrile

The phenomenon of excited state twisted intramolecular charge transfer (TICT) process in N,N-dimethylaminonaphthyl-(acrylo)-nitrile (DMANAN) has been reported on the basis of steady-state absorption and fluorescence spectroscopy in combination with quantum chemical calculations. The absorption and fluorescence characteristics of DMANAN in solvents of different polarity reveal the presence of a single species in the ground state which forms the intramolecular charge transfer state upon photoexcitation. The observed dual fluorescence is assigned to a high-energy emission from the locally excited or the Franck-Condon state and the red-shifted emission from the charge transfer (CT) state. In polar protic solvents, hydrogen-bonding interaction on CT emission has been established from the linear dependency of the position of the low-energy emission maxima on hydrogen-bonding parameter (α). The experimental findings have been correlated with the theoretical results based on TICT model obtained at density functional theory (DFT) level. The theoretical potential energy surface for the first excited state along both the donor and acceptor twist coordinates in the gas phase obtained by time dependent density functional theory (TDDFT) method and in polar solvent by time dependent density functional theory-polarized continuum model (TDDFT-PCM) method predicts well the experimental spectral properties.     

Fourier-transform microwave spectroscopy of N-methylaniline

The jet-cooled Fourier-transform microwave spectrum of N-methylaniline (C₆H₅-NHCH₃) was recorded in the region of 10-26 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Furthermore, a Coriolis-like coupling parameter characterizing an interaction between an internal rotation of a methyl group and an overall rotation was also determined from A-E splittings observed in pure rotational transitions with high K_a values. The Coriolis-like coupling parameter permitted the determination of the barrier to internal rotation of the methyl group which was found to be 975 cm⁻¹.     

Integrable deformations of Lotka-Volterra systems

The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map Δ(2) that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found.     

Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem

Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Some direct formal and practical implications of the present reformulation of DFT are also discussed.     

Effect of annealing temperature on microstructure, hardness and adhesion properties of TiSixNy superhard coatings

A series of TiSi_xN_y superhard coatings with different Si contents were prepared on M42 steel substrates using two Ti and two Si targets by reactive magnetron sputtering at 500 °C. These samples were subsequently vacuum-annealed at 500, 600, 700, 800 and 900 °C, respectively. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), microindenter, Rockwell hardness tester and scratch tester were applied to investigate the microstructure, phase configuration, hardness and adhesion properties of as-deposited and annealed samples. The results indicated that there were two bonds, TiN and Si₃N₄, in all presently deposited TiSi_xN_y thin films, that structure was nanocomposite of nanocrystalline (nc-) TiN embedded into amorphous Si₃N₄ matrices. Annealing treatment below 900 °C played a little role in microstructure and hardness of the coatings although it greatly affected those of steel substrates. The film-substrate adhesion strength was slightly increased, followed by an abrupt decrease with increasing annealing temperature. Its value got to the maximum at 600 °C. Annealing had little effect on the friction coefficient with its value varying in the range of 0.39-0.40.     

Global fittings of NNO and NNO vibrational-rotational line positions using the effective Hamiltonian approach

An effective Hamiltonian built up to sixth order in the Amat-Nielsen ordering scheme describing all rovibrational energy levels in the ground electronic state and containing in explicit form all resonance interaction terms due to the approximate relations between harmonic frequencies ω₁≈2ω₂ and ω₃≈4ω₂ was applied to model the observed rovibrational line positions (collected from the literature) of ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O isotopologues of nitrous oxide. For ¹⁴N¹⁵N¹⁶O, 124 effective Hamiltonian parameters were fitted to near 28 000 observed line positions covering the 0.8-8860 cm⁻¹ spectral range. The RMS of the weighted fit is 0.00126 cm⁻¹ and dimensionless standard deviation is 1.48. For ¹⁵N¹⁴N¹⁶O, 121 effective Hamiltonian parameters were fitted to more than 31 000 observed line positions covering the same spectral interval. The RMS of the weighted fit is 0.00185 cm⁻¹ and dimensionless standard deviation is 1.85. In both cases the models describe all available line positions with precision compatible to the measurement uncertainties. A number of local resonance perturbations was found and discussed. Among these perturbations there are interpolyad resonance Coriolis interactions. A comparison of HITRAN-2008 data with the calculations based on the fitted models is presented.     

Ab initio study of phase stability,thermodynamic and elastic properties of C3N2 derived from cubic C20

In this work, we report a quite different conclusion from Tian et al. [Phys. Rev. B 78 (2008) 235431]. It is proved that β-C₃N₂ is the only phase under high pressure, and α-C₃N₂ does not exist. β-C₃N₂ is a covalent crystal composed of strong CC and CN covalent bonds. Band gap of β-C₃N₂ increases with pressure. The width of antibonding state, shown in partial density of states (PDOS), keeps about 5 eV with rising pressures, which brings stable CN or CC covalent bonds. At sufficiently low temperatures, heat capacity (C_v) is proportional to T³; and at intermediate temperatures, C_v is governed by the details of vibrations of the atoms; finally, C_v reaches to β-C₃N₂'s Dulong–Pettit limit (about 120 J/mol K). Though thermal expansion coefficient (α) increases with temperature, α is less than 1×10⁻⁵ K⁻¹. Elastic constants rise with pressure, but shear moduli is quite steady which increases just a little with pressures.     

Population analysis solution to hardness enhancement in TiCxN1−x

We investigated the hardness enhancement in titanium carbonitrides (TiC_xN_1−x) by the population analysis method based on first-principles calculations. Populations for bonds TiC and TiN in TiC_xN_1−x (0.25<x<0.75) are all positive. The enhanced hardness for titanium carbonitrides is well explained by overlap population analysis. Intrinsic hardness of TiC_xN_1−x has been calculated based on the obtained overlap populations. The calculated results are in good agreement with the available experimental data.     

A note on loop-soliton solutions of the short-pulse equation

It is shown that the N-loop soliton solution to the short-pulse equation may be decomposed exactly into N separate soliton elements by using a Moloney-Hodnett type decomposition. For the case N=2, the decomposition is used to calculate the phase shift of each soliton caused by its interaction with the other one. Corrections are made to some previous results in the literature.     

Extended supersymmetry in massless conformal higher spin theory

We propose superfield equations in tensorial N-extended superspaces to describe the N=2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended tensorial superspace. The N-extended higher spin supermultiplets just contain scalar and ‘spinor’ fields in tensorial space so that, in contrast with the standard (super)space approach, no nontrivial generalizations of the Maxwell or Einstein equations to tensorial space appear when N>2. For N=4,8, the higher spin-tensorial components of the extended tensorial superfields are expressed through additional scalar and spinor fields in tensorial space which obey the same free higher spin equations, but that are axion-like in the sense that they possess Peccei-Quinn-like symmetries.