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.     

The structure of the Q-family of mappings of the n-representability theory I

A family of mappings, extending the Q- and B-mappings of the n-representability theory, is derived.     

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.     

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.     

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.     

Subsidiary conditions and physical S-matrix unitarity in indefinite-metric quantum gravitation theory

The quantum theory of gravitational fields is formulated in a manifestly Lorentz covariant manner in the framework of indefinite-metric quantum field theory. The physical state subspace is defined by the two subsidiary conditions Q_B|phys〉 = Q_c|phys〉 = 0, where the conserved charges Q_B and Q_c are the generators of the BRS transformation ond of the Faddeev-Popov ghost scale transformation, respectively. By clarifying the metric structures of the Fock space of asymptotic fields with help of the Ward-Takahashi identities, the physical S-matrix unitarity is established in just the same way as in the canonical theory of Yang-Mills fields.     

Covariant quantization of string based on BRS invariance

Covariant canonical quantization of the bosonic string is performed, based on the BRS invariance principle. Defining a physical state by a modified form of Kugo-Ojima's subsidiary condition Q_B|phys〉 = 0 (Q_B = BRS charge), we prove a no-ghost theorem in a simple manner. There an interesting relation between critical dimension and BRS symmetry is noticed; namely, the conditions D = 26 and α₀ = 1 for the space-time dimension D and the zero-intercept α₀ of leading trajectory are required by the nilpotency Q_B² = 0 of the BRS charge. In addition, ghost number fractionization is observed in this system.     

Density functional theory: Foundations reviewed

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N$N$-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N$N$-representability conditions on the 2-RDM have recently been attained.     

Modulation instability of dispersive electromagnetic waves in a Josephson junction in a finite-thickness plate

Modulation instability of finite-amplitude dispersive electromagnetic waves is studied in the framework of nonlocal electrodynamics of a Josephson junction in a finite-thickness plate. The dispersion equation is derived for the increment of small amplitude perturbations. For this type of waves, the regions of development of modulation instability and stability of waves are determined. It is shown that modulation instability of waves develops in a finite range of wavevectors Q _B1(k, D, L) < Q < Q _B2(k, A, D, L), while waves are stable in the important long-wave region 0 ≤ Q ≤ Q _B1(k, D, L) and for Q ≥ Q _B2(k, A, D, L). The unique possibility of controlling the modulation instability region by dispersion parameter k, viz., the wave vector (or frequency ω(k)) of the modes in the linear approximation.     

Functional self-similarity,scaling and a renormalization group calculation of the partition function for a non-ideal chain

The hypothesis of asymptotic self-similarity for nonideal polymer chains is used to derive the functional and differential equations of a new renormalization group. These equations are used to calculate the partition functions of randomly jointed chains with hard-sphere excluded-volume interactions. Theoretical predictions are compared with Monte Carlo calculations based on the same microscopic chain model. The excess partition function converges very slowly to its true asymptotic form δQ(N→∞)∼κ^N−1. The conventional asymptotic formula, δQ(N→∞)∼κ^N−1N^γ−1, is found to be applicable for chains of moderate length and for excluded-volume interactions appropriate to the subclass of flexible self-avoiding chains.     

13C−1H heteronuclear dipolar correlation studies of the hydrogen bonding of the quinones inRhodobacter sphaeroides R26 reaction centers

The photosynthetic reaction center (RC) of the photosynthetic bacteriumRhodobacter sphaeroides R26 contains two quinones, Q_A and Q_B. Solid-state heteronuclear (¹H?¹³C) dipolar correlation spectroscopy has been used to study the binding of the quinones in the ground state for RCs reconstituted with l-¹³C ubiquinone-10. Lee-Goldburg cross-polarization buildup curves are recorded to determine distancesr _CH between the l-¹³C carbon labels and the protons involved in the polarization transfer. The l-¹³C of both Q_A and Q_B have intermolecular correlations with protons that resonate downfield, in the region of hydrogen-bonding protons. The distances between the carbon labels and the correlated protons are short, 0.21±0.01 nm. Hence the nuclear magnetic resonance provides evidence for strong hydrogen-bonding interactions at the l-C=O of both Q_A and Q_B for RCs in the ground state. The environment of the l-¹³C of the Q_B is structurally heterogeneous compared to that of the Q_A. The data can be reconciled with a strong H-bonding interaction of the l-C=O of Q_A with Ala M260 NH, and with complex hydrogen bonding involving NH of Ile-L224 and of Gly-L225, and possibly the Ser-L223 hydroxyl group of the l-C=O of the Q_B, in the proximal site.     

QCD cascade model in deep inelastic scattering

We develop a new QCD cascade model for jets in deep inelastic scattering. We use the light-like axial gauge whose gauge vector is parallel to momentum of the initial parton so that only final partons cascade. Due to this feature we can generate events for any given virtualityQ ² andx _B =Q ²/2Pq.     

Systematic behavior ofB(E2) values in the yrast bands of doubly even nuclei

The experimental information onB(E2) transition rates in the yrast bands of doubly even nuclei (126≦A≦184) is systematized. The strength functionS _exp≡B(E2,I→I?2)×E(I→I?2) is found to reveal characteristic behavior significant for structure studies of yrast bands. The energy-weightedB(E2,I→I?2) values (S _exp) and 2?/?²(?: moment of inertia) are plotted versus the rotational frequency squared ?²ω² for each nucleus. In strongly deformed nuclei (N≧90), theS _exp curves smoothly increase for low rotational frequencies suggesting that up to spin valuesI≈8 the ratioQ ₀ ² ? is nearly constant (Q ₀: quadrupole moment). This is not the case in nuclei with a soft core (N≦88). In the relevant discussion, the hydrodynamical model as well as the CAP effect are considered. The results in the backbending region are qualitatively discussed in terms of the two-band crossing model. Evidence is found supporting the prediction of an oscillating behavior of the yrast-yrare interaction.     

Relativistic many-body calculation of parity-violating E1-amplitude for the 6S → 7S transition in atomic cesium

The parity violating E1-amplitude for the 6S–7S transition in cesium has been calculated from first principles: $\text{〈7S|D}{}_{\mathrm{z}}\text{|6S〉 = (0.88 ± 0.03) × 10}{}^{\mathrm{?11}}\text{(}\text{?Q}{}_{\mathrm{W}}\text{N}\text{)(?iea}{}_{\mathrm{B}}\text{)}$, where Q_W is the weak nuclear charge, N is the number of neutrons, and a_B is The Bohr radius. The experimental data from Bouchiat et al. make it possible to find Q_W = ?73.4 ± 8.1 ± 6 and the Weinberg angle sin²θ_W = 0.237 ± 0.036 ± 0.03. To control the accuracy, the energy levels, the fine and hyperfine structure intervals and the oscillator strenghts in the S-P transitions in Cs have been calculated.     

On Eigenvalues of the Sum of Two Random Projections

We study the behavior of eigenvalues of matrix P _N +Q _N where P _N and Q _N are two N-by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal behavior of eigenvalues for large N. The limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the Bessel or the Airy kernel at the edge depending on parameters. We also study an exceptional case when the local behavior of eigenvalues of P _N +Q _N is not universal in the usual sense.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Dissociation activation barrier and heat of chemisorption: A morse-type analytical approach

The activation barrier ΔE¹_ABfor dissociation AB → A + B on transition-metal surfaces is analyzed within an additive Morse-type approach based on the bond-order conservation. It is shown that $\text{Δ}\text{E}{}^1{}_{\mathrm{AB}}\text{=}\text{D}{}_{\mathrm{AB}}\text{?(}\text{Q}{}_{\mathrm{A}}\text{+}\text{Q}{}_{\mathrm{B}}\text{+}\text{Q}{}_{\mathrm{A}}\text{Q}{}_{\mathrm{B}}\text{/(}\text{Q}{}_{\mathrm{A}}\text{+}\text{Q}{}_{\mathrm{B}}\text{)}$ where D_AB is the gas-phase dissociation energy and Q_A(Q_B) is the heat of atomic chemisorption. Estimates of $\text{Δ}\text{E}{}^1\text{for H}{}_2\text{, N}{}_2\text{, O}{}_2$, and NO are shown to be in reasonable agreement with experiment. The two-dimensional potential diagram of the metal-AB interactions is defined analytically and discussed in some detail.     

SU(3) implications of the observation of the A1 and C mesons

A new determination of the Q_A?Q_B mixing angle and of the antisymmetric coupling for the vector-pseudoscalar decay of the axial vector mesons is presented. This uses information from the decay rates of the A₁ and C mesons found in the study of baryon exchange processes in K^?p interactions at 4.2 GeV/c combined with the decay rate B → ωπ. The consistency between the results obtained from backward produced A₁ and C and diffractively produced Q₁ and Q₂ is discussed.     

The primary and secondary acceptors in bacterial photosynthesis III. Characterization of the quinone radicals Q A − ⋅ and Q B − ⋅ by EPR and ENDOR

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques were used to investigate the electronic structure of the primary (Q _A ^?? ) and secondary (Q _B ^?? ) ubiquinone electron acceptors in reaction centers (RCs) of the photosynthetic bacteriumRhodobacter sphaeroides. To reduce the EPR linewidth, the high-spin Fe²⁺ present in native RCs was replaced by diamagnetic Zn²⁺. Experiments were performed both on frozen solutions and single crystals at microwave frequencies of 9, 35 and 94 GHz. Differences in the EPR/ENDOR spectra were observed for Q _A ^?? and Q _B ^?? , which are attributed to different environments of the quinones in the RC. The differences exhibited themselves in: (i) the g-tensors, (ii) the¹⁷O and¹³C hyperfine coupling (hfc) constants of the quinones labeled at the carbonyl group, (iii) the¹H-hfcs of the quinone ring and (iv) the exchangeable protons hydrogen bonded to the carbonyl oxygens. From these results and from H/D exchange experiments, the following conclusions were drawn: both Q _A ^?? and Q _B ^?? have at least two hydrogen bonds of different strengths to the carbonyl oxygens. The hydrogen bonds for Q _A ^?? are stronger and more asymmetric than for Q _B ^?? . For Q _A ^?? the stronger bond (to O₄) was assigned to His(M219) and the weaker (to O₁) to Ala(M260). For Q _B ^?? the stronger bond (to O₄) was assigned to His(L190), with several weaker bonds (to O₁) to Ser(L223), Ile(224) and Gly(L225). From the temperature dependence of the hfcs of the exchangeable protons some dynamic properties of the RC were deduced. Hfcs with more distant nitrogens were observed by electron spin echo envelope modulation (ESEEM). For Q _A ^?? they were assigned to N_δ of His(M219) and to the peptide backbone nitrogen of Ala(M260) and for Q _B ^?? to N_δ of His(L190). These interactions indicate the extent of the electron wave function, which is important for the understanding of the electron transfer mechanism. Based on the magnetic resonance results, the function of the quinone acceptors in the reaction center is discussed.     

Extensions of string theories

With the motivation that critical dimensionsD≠4 might be suggesting that string theories have not been completely formulated, we study more general alternatives. We first consider a direct extension in the world-sheet formulation withN _B bosons andN _F fermions and analyze the conditions for canceling the anomaly in all possible combinations ofN _B ,N _F andD. Later on we incorporate degrees of freedom of antisymmetric tensors to the previous model. The only possibility to cancel the anomaly in this case is withN _B =N _F =1 and the our everyday spacetime dimensionD=4.