Tensor representations of conformal algebra and conformally covariant operator product expansion

A conformally covariant formulation of operator product expansion is discussed as an expansion of the product of two representations into a direct sum of irreducible representations. The basic irreducible representations are analyzed and classified. The isomorphism between the conformal algebra and the O(4, 2) algebra is used to obtain a manifestly covariant formalism. The implications of the isomorphism in the derivation of the representations is discussed. The covariant O(4, 2) formalism directly relates dominant terms to nondominant terms in the light-cone limit. The essential coincidence of the problem of a conformal covariant operator product expansion to the problem of determining the form of the three-point function is stressed, together with the relevance of a selection rule for two-point functions following from exact (not spontaneously broken) conformal covariance. The role of Ward identities in a conformal covariant scheme is pointed out, and the mathematical implications on the n-point functions from causality are described.     

Solving general gauge theories on inner product spaces

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form ph〉 = exp [Q, ψ]ph〉₀ where Q is the nilpotent BRST operator, ψ a hermitian fermionic gauge-fixing operator, and ph〉_o BRST invariant states determined by a hermitian set of BRST doublets in involution. ph〉₀ does not belong to an inner product space although ph〉 does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for ph〉₀ and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that ph〉₀ are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set ph〉₀ are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.     

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.     

Quantum states transfer between coupled fields

We study the exchange of states in coupled fields along their time evolution. The coupling is described by a quadratic form in terms of annihilation and creation operator in the field Hamiltonian. An analytical approach is employed to describe the time evolution of the field state in Fock's space and the conditions for an arbitrary initial states to be transferred with 100% fidelity is determined. We show that only for initial states C₀|0>+C_N|N>, this situation can occurs. The important |1〉↔|0〉 qubits transfer is a particular case of this transference of number state. The relation between the coupling constant and characteristic field frequencies for complete state transference is also determined.     

Precise model approximation of JINR (Dubna) data on nuclear level densities in the region 40 ≤ <Emphasis Type="Italic">A</Emphasis> ≤ 200 below <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The experimental nuclear level density below the neutron binding energy B _n in the mass region 40 ≤ A ≤ 200 is approximated to a high precision on the basis of the Strutinsky model combined with the assumption that the coefficient of collective enhancement of the level density for a given number of excited quasiparticles decreases exponentially with increasing excitation energy. This combination of model concepts makes it possible to reproduce faithfully not only the general trend revealed by the method developed at the Joint Institute for Nuclear Research (JINR, Dubna) in the change in the level density with increasing excitation energy in any nuclei but also the fine structure of this level density. Realistic experimental information about the change in the relationship between the densities of quasiparticle- and vibrational-type states was obtained for the first time for any nuclei virtually up to the neutron binding energy B _n .     

Magnetic properties of a Na-doped WS<Subscript>2</Subscript> monolayer in the presence of an isotropic strain

The magnetic properties of Na-doped WS₂ monolayer under strain are investigated by ab initio methods. Without strain, the Na-doped WS2 monolayer is a magnetic nanomaterial and the total magnetic moment is about 1.07μ_B. We applied strain to Na-doped WS₂ monolayer from–10% to 10%. The magnetic properties are modified under different strain; the doped system gets a maximum value of at 2.01μ_B 10% tensile strain and a minimum value of at 0μ_B–10% compressive strain. The coupling between 3p states of S and 5d states of W is responsible for the strong strain effect on the magnetic properties. Our studies predict Na-doped WS₂ monolayer under strain to be candidates for application in spintronics.     

Millimeter wave spectrum of HCS+1

High-resolution Fourier transform spectra have been used to measure precisely the line positions and intensities of the K′_a = 0–12 stacks of the ν₁ band of ¹⁴N¹⁶O₂ in the 1200–1850 cm^?1 region. Using a Hamiltonian which explicitly takes into account the Coriolis resonances between the (0 0 1) state and the (1 0 0) and (0 2 0) states, it has been possible to reproduce satisfactorily the rotational energy levels of the three interacting states {(0 2 0), (1 0 0), (0 0 1)} of ¹⁴N¹⁶O₂. An improved set of spin-rotation, rotational, and Coriolis coupling constants was determined for these three interacting states. In particular, we have been able to determine, for the (1 0 0) state, asymmetry-dependent constants such as (B - C) and (?_bb ? ?_cc) which could not be obtained in the previous work concerning the ν₁ band by M. Laurin and A. Cabana (J. Mol. Spectrosc.69, 421–434 (1978)). In addition, individual intensities of transitions belonging to the ν₁ band were measured, leading to the precise determination of the vibrational part of the transition moment operator of the ν₁ band together with five correcting rotational terms appearing in the expansion of this operator.     

Eigenvalue problem for arbitrary linear combinations of a boson annihilation and creation operator

The eigenvalue problem for arbitrary linear combinations kα + μα^? of a boson annihilation operator α and a boson creation operator α^? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α^? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α^? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter.     

First principles study on the structural,electronic and phonon properties of monolayer B2Si

Using first principles density functional theory, we predict a monolayer B₂Si structure with space group Pmm2 in the present work. This structure is confirmed to be dynamically stable. Based on the plane wave pseudopotential approach, the charge density, electron localization function, density of states, energy band, phonon property and thermal conductivity of Pmm2-B₂Si are systematically studied. It is interesting that the sp² hybridization and coordination bond of Si are found in Pmm2-B₂Si, which is the most important factor for its structural stability. The density of states and energy band analysis reveals that Pmm2-B₂Si is metallic because of the partial occupied Si 3pz and B 2pz states. Moreover, the acoustic-optical coupling is important for phonon transport in Pmm2-B₂Si, and the contribution of optical modes to the lattice thermal conductivity along the [100] and [010] directions is 13% and 12%, respectively. This study gives a fundamental understanding of the structural, electronic and phonon properties in Pmm2-B₂Si.     

On converse to Koopman's Lemma

Koopman's Lemma states that if a flow T_t is measure preserving for a measure μ on a constant energy surface Ω, then the flow generates a one parameter family of unitary operators U_t on L² (Ω, μ). We show here a converse, namely that under certain (physically motivated) conditions a unitary operator family U_t can be made to generate a corresponding underlying family T_t of point transformations. This result comes out of questions of independent interest in the study of relationships between reversibility and irreversibility, and has application to the foundations of statistical mechanics. In particular, it establishes the principle often used intuitively in chemistry that a forward moving (e.g., Markov) process that loses information cannot be reversed. In a different setting, it provides the answer to a question in the representation theory of isometries on L^p spaces a Banach-Lamperti theorem). These results also allow an interesting reformulation of Ornstein's isomorphism theorem on Bernoulli systems.     

Determination of fixed points and shift cycles for nearest neighbor cellular automata

One-dimensional nearest neighbor cellular automata defined over Z₂ are characterized in terms of a set of eight nonadditive basis operators which act on the automaton state space. Every evolution rule for such automata can be expressed as an operator which is a direct sum of the basis operators. This approach allows decomposition of automata rules into additive and nonadditive parts. As a result, it is simple to determine fixed points (those states for which the rule reduces to the identity), and shift cycles (sets of states on which the rule reduces to a shift). Sets of states on which any given nearest neighbor automaton reduces to an identity or a shift are characterized. This allows us to obtain some results on the entropic properties of nonadditive automata, although these are not nearly so complete as results obtained for additive automata.     

Temperature dependent lineshape changes in solid H2 for low oH2 concentrations

The nmr lineshape due to unpaired oH₂ molecules in solid pH₂ changes significantly below 0.2 K. A deconvolution of lineshape based on a mitional narrowing model yields the relative amplitude of the part of the signal showing resolved structure as well as the temperature dependence of the frequency determining parameter. Both the relative amplitude of this signal and the temperature at which structure appears decrease with increasing oH₂ concentration.     

The group theoretic structure of the dual current vertex

We construct the Corrigan-Fairlie dual current vertex using an intertwining operator. This first necessitates the development of an isomorphism between certain function and Fock space representations of the two-dimensional conformal group. The intertwining operator is a mapping between the different representations and may then be constructed using an analogous procedure. Due to the group properties built into this operator the well-known gauge conditions obeyed by the vertex soon follow.     

Minimal-disturbance measurement as a specification in von Neumann's quantal theory of measurement

In von Neumann's theory an incomplete observableA is measured by measuring any complete observableB whose functionA is. This procedure is narrowed down in this paper by the additional requirement of preservation of the sharp value of any observable compatible withA. The requirement is shown to be equivalent to the unique change of state:ρ → (trρP _n)^?1 P _nρP_n (P _n is the eigenprojector ofA corresponding to the obtained eigenvaluea _n, ρ is the statistical operator of the initial state, and by assumption trρP _n > 0). This characterises the minimal-disturbance measurement. A necessary and sufficient condition is derived for the selection of the above observableB so that its measurement implies the minimal-disturbance measurement ofA. For arbitraryρ andA, there exists aB satisfying the condition. Hence, this constitutes a reasonable specification within von Neumann's theory, reducing the latter to the physically preferable minimal-disturbance measurement theory.     

Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.     

Theoretical study of magnetism in RM12B6 compounds (R=Y,La or Ce; M=Fe,Co)

Electronic structure study for RM₁₂B₆ intermetallics (R=Y, La or Ce; M=Fe, Co) was performed. Fixed spin moment calculations for different volumes of unit cell were used to find low and high moment states in LaFe₁₂B₆. Obtained results are in agreement with previously obtained experimental and theoretical results. Total magnetic moments obtained for YCo₁₂B₆ and LaCo₁₂B₆ are in fair agreement with experimental values. In CeCo₁₂B₆ discrepancy between theory and experiment seems to be more pronounced. It seems that the calculated Co magnetic moments could be overestimated in the studied RCo₁₂B₆ compounds. Present calculations indicate that Fe (Co) atoms prefer 18(h) (18(g)) atomic positions what is in agreement with experiment.     

Reasons for the failure of formal scattering formulas in systems having no bound states

Reasons for the failure of formal scattering formulas in systems having no bound states are that due to the non-zero ground-state energy of H, the map of the Møller operator from the free space of H₀ onto the space of H cannot be one-to-one. An unusual number of mistakes about this problem in a recently published paper by Muga and Veguillas are also indicated.     

Structural anomalies associated with the electronic and spin transitions in LnCoO<Subscript>3</Subscript>

A powder X-ray diffraction study, combined with magnetic susceptibility and electric transport measurements, was performed on a series of LnCoO₃ perovskites (Ln = Y, Dy, Gd, Sm, Nd, Pr and La) over a temperature range 100–1000 K. A non-standard temperature dependence of the observed thermal expansion was modelled as a sum of three contributions: (1) weighted sum of lattice expansions of the cobaltite in the diamagnetic low spin state and in the intermediate (IS) or high (HS) spin state. (2) An anomalous expansion due to the increasing population of excited (IS or HS) states of Co³⁺ ions over the course of the diamagnetic-paramagnetic transition. (3) An anomalous expansion due to excitations of Co³⁺ ions to another paramagnetic state accompanied by an insulator-metal transition. The anomalous expansion is governed by parameters that are found to vary linearly with the Ln ionic radius. In the case of the first magnetic transition it is the energy splitting E between the ground low spin state and the excited state, presumably the intermediate spin state. The energy splitting E, determined by a fit to magnetic susceptibility, decreases with temperature. The values of E determined for LaCoO₃ and YCoO₃ at T=0 K are 164 K and 2875 K respectively, which fall to zero at T=230 K for LaCoO₃ and 860 K for YCoO₃. The second anomalous expansion connected with a simultaneous magnetic and insulator-metal transition is characterized by its center at T=535 K for LaCoO₃ and 800 K for YCoO₃. The change of the unit cell volume during each transition is independent of the Ln cation and is about 1% in both cases.     

Vibronic coupling and excited‐state reaction dynamics of pyrazine in 1 1B2u (1ππ*) state by resonance Raman spectroscopy and CASSCF calculation

The photophysics and photochemistry of pyrazine (C₄H₄N₂, D_2h) after excitation to the S₂ (1 ¹B_2u, ¹ππ*) electronic state were studied by using the resonance Raman spectroscopy and complete active space self‐consistent field method calculations. The B‐band resonance Raman spectra in cyclohexane solvent were obtained at 266.0, 252.7, and 245.9 nm excitation wavelengths to probe the structural dynamics of pyrazine in the S₂ (1 ¹B_2u, ¹ππ*) state. Three electronic states 1 ¹B_3u, 1 ¹B_1g, and 1 ¹B_2g were found to couple with the S₂ (1 ¹B_2u, ¹ππ*) state. Two conical intersection (CI) points CI[S₂(B_2u)/S₁(B_3u)] and CI[S₁/S₀] and one transition state of the isomerization between pyrazine and pyrimidine were predicted to play important roles in the photochemistry of pyrazine. On the basis of the calculations, the mechanism of the photoisomerization reaction between pyrazine and pyrimidine has been proposed. Copyright © 2012 John Wiley & Sons, Ltd.