Structural, elastic, electronic and magnetic properties of ThCr2Si2 from first-principles calculations

The tetragonal (s.g. I4/mmm; #139) ThCr₂Si₂ is widely known as a structural type of the broad family of the so-called 122-like ternary phases which includes now more than 800 members. Among them the superconducting iron-pnictides (discovered in 2008, -earth metals) and the newest superconducting iron-chalcogenides (discovered in 2010, metals) have attracted recently enormous interest in this class of materials. Meanwhile, the data about the electronic, magnetic, and elastic properties of the ThCr₂Si₂ phase itself are still practically absent. Here, by means of first-principles calculations, the optimized structural parameters, spin ordering of the magnetic ground state, independent elastic constants, bulk, shear, and Young’s moduli, elastic anisotropy indexes, total and partial densities of states, and inter-atomic bonding picture for ThCr₂Si₂ were obtained for the first time and analyzed in comparison with the aforementioned most popular 122-like systems and .     

Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method

We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation vectors, their linear (in)dependence and the spectrum of Lyapunov exponents. The different time evolution of these volumes can be used to identify rapidly and efficiently the nature of the dynamics, leading to the introduction of quantities that clearly distinguish between chaotic behavior and quasiperiodic motion on N-dimensional tori. More specifically we introduce the Generalized Alignment Index of order k () as the volume of a generalized parallelepiped, whose edges are k initially linearly independent unit deviation vectors with respect to the orbit studied whose magnitude is normalized to unity at every time step. We show analytically and verify numerically on particular examples of N-degree-of-freedom Hamiltonian systems that, for chaotic orbits, tends exponentially to zero with exponents that involve the values of several Lyapunov exponents. In the case of regular orbits, fluctuates around non-zero values for 2≤k≤N and goes to zero for N<k≤2N following power laws that depend on the dimension of the torus and the number m of deviation vectors initially tangent to the torus: ∝t^{−2(k−N)+m} if 0≤m<k−N, and ∝t^−(k−N) if m≥k−N. The is a generalization of the Smaller Alignment Index (SALI) (). However, provides significantly more detailed information on the local dynamics, allows for a faster and clearer distinction between order and chaos than SALI and works even in cases where the SALI method is inconclusive.     

Theory of antiferromagnetic exchange interaction for mixed-valent FeFe spin cluster in model complex of semimethemerythrin

The antiferromagnetic phenomena of both mixed valent Fe^IIIFe^II spin clusters and homodinuclear Fe^IIIFe^III clusters in complexes have been studied by means of our covalent magnetic exchange theoretical method. The sensitive relations between the exchange parameter J and the covalent factors N_A (for Fe^III) and N_B (for Fe^II) and the Fe?Fe separation R have been derived by use of our double-Slater function calculation procedure, the corresponding theoretical curve of J vs. N_A,N_B and R has been obtained. By taking the typical covalent factors of Fe^III and Fe^II, and using the observed Fe-O bond lengths: for Fe^III-O-Fe^II cluster in model complex {[Fe(acacen)]₂ONa}₂; for Fe^III-O-Fe^III cluster in oxyhemerythrin, we obtained the theoretical values: for Fe^III-O-Fe^II cluster and for Fe^III-O-Fe^III cluster. These are in good agreement with the corresponding experimental findings in {[Fe(acacen)]₂ONa}₂ and in oxyhemerythrin, respectively.     

Integrable perturbations of the N-dimensional isotropic oscillator

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h₆-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N−1) ‘Rosochatius’ terms that preserve the complete integrability of all these models.     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

Measurement of ultraweak transitions in the visible region of molecular oxygen

A highly sensitive cavity-enhanced frequency modulation spectroscopy technique has been used to measure ultraweak transitions in molecular oxygen that had not previously been characterized. The self-broadened half-width and line intensity of the measured transitions are reported. We include 12 high J transitions in the band of ¹⁶O₂ (the so-called A band), 59 transitions in the hot band of ¹⁶O₂, and 17 high J transitions in the band of ¹⁶O¹⁸O. Our measurements of line positions of the ¹⁶O¹⁸O transitions are used to determine improved molecular constants for the excited state of ¹⁶O¹⁸O.     

Microwave study of the rotational spectrum of oxygen molecule in the range up to 1.12 THz

Microwave study of the rotational transitions of oxygen molecule in its electronic and vibrational ground states is reported. Eight transitions belonging to N=3-1, N=5-3, and N=7-5 groups were investigated. Central line frequencies and pressure broadening parameters for O₂ and N₂ as perturbers were determined. The highest frequency of measured transition (N,J)=(7,6)-(5,6) has been 1.12 THz. Spectrometer with backward wave oscillator (BWO) and acoustic detector (RAD) was used. Since this experiment has more than doubled the number of previously measured rotational lines of oxygen molecule and better accuracy was achieved, the fitting of new set of rotational transition frequencies has been performed and new more accurate molecular constants for in , v=0 state have been obtained.     

Sufficient and necessary condition of separability for generalized Werner states

In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain a sufficient and necessary condition for the separability of a specific class of N d-dimensional system (qudits) states, namely special generalized Werner state (SGWS): , where is an entangled pure state of N qudits system and α_i satisfies two restrictions: (i) ; (ii) Matrix , where , is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.     

Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles

The N-dimensional Hamiltonian

     

Equation of state of cubic hafnium(IV) nitride having Th3P4 -type structure

Pressure dependence of the specific volume, V(P), of the recently discovered high-pressure compound Hf₃N₄ having cubic Th₃P₄-type structure (c- Hf₃N₄) has been measured at room temperature up to 43.9 GPa in a diamond anvil cell using energy-dispersive X-ray powder diffraction combined with synchrotron radiation. A least-square fit of the Birch-Murnaghan equation of state to the experimental V(P)-data yielded for c- Hf₃N₄ the bulk modulus of and its first pressure derivative of . For fixed at 4 the bulk modulus of c- Hf₃N₄ was determined to be . The obtained B₀-value is only insignificantly below that estimated in preliminary measurements. Existing theoretical predictions for B₀ scatter around the present experimental data. The observation of a high bulk modulus of c- Hf₃N₄ supports the suggestion that this compound could have high hardness.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

High-resolution rovibrational study of the Coriolis-coupled ν12 and ν15 modes of [1.1.1]propellane

Infrared spectra of the small strained cage molecule [1.1.1]propellane have been obtained at high resolution (0.0015 cm⁻¹) and the J, K, and l rovibrational structure has been resolved for the first time. We recently used these spectra to obtain combination-differences to deduce ground state parameters for propellane; over 4100 differences from five fundamental and four combination bands were used in the fitting process. The combination-difference approach eliminated potential errors caused by localized perturbations in the upper states and gave well-determined ground state parameters. In the current work, these ground state constants were fixed when fitting the upper state parameters for the ν₁₂ (e′) perpendicular and parallel bands. Over 4000 infrared transitions were fitted for each band, with J, K values ranging up to 71, 51 and 92, 90, respectively. While the transition wavenumbers for both bands can be fit nicely using separate analyses for each band, the strong intensity perturbations observed in the weaker ν₁₂ band indicated that Coriolis coupling between the two modes was significant and should be included. Due to correlations with other parameters, the Coriolis coupling parameter for the ν₁₅ and ν₁₂ interaction is poorly determined by a transition wavenumber fit alone but, fortunately, the intensity perturbations gave useful added constraints on . By combining the wavenumber fit with a fit of experimental intensities, a value of −0.42 was obtained, quite close to the value of −0.44 predicted by Gaussian ab initio density functional calculations using a cc-pVTZ basis. This intensity fit also yielded a (∂μ^z/∂Q₁₅)/(∂μ^x/∂Q_12a) dipole derivative ratio of 36.5, in reasonable agreement with a value of 29.2 predicted by the ab initio calculations. This ratio is unusually high due to large charge movement as the novel central C_axial-C_axial bond is displaced along the symmetry axis of the molecule for the ν₁₅ mode.     

Prospects of reactor neutrino experiments

Since the energy of a reactor neutrino is a few MeV, all , and oscillations are accessible by reactor neutrino experiments. KamLAND observed the oscillation and currently Double Chooz, RENO and Dayabay experiments are under construction aiming to detect oscillation. There are still good prospects for future reactor neutrino experiments after them. For example, there is room to further improve sin²2θ₁₃ accuracy at a baseline of ∼1.5 km, a very precise sin²2θ₁₂ measurement and the determination of mass hierarchy may be possible at a baseline ∼50 km, and if KamLAND is enlarged to the SuperKamiokande size, better measurement of and sin²2θ₁₂ will be anticipated. It is important to take into account such possibilities when planning future neutrino program after θ₁₃ is measured by current experiments.