State Property Systems and Orthogonality

The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva–Brussels approach to the foundations of quantum mechanics (Aerts, D. International Journal of Theoretical Physics, 38, 289–358, 1999; Aerts, D. in Quantum Mechanics and the Nature of Reality, Kluwer Academic; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B. International Journal of Theoretical Physics, 38, 359–385, 1999), and the category of state property systems was proven to be equivalent to the category of closure spaces (Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., International Journal of Theoretical Physics, 38, 359–385, 1999; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., The construct of closure spaces as the amnestic modification of the physical theory of state property systems, Applied Categorical Structures, in press). The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the T₀ and T₁ axioms of closure spaces (van Steirteghem, B., International Journal of Theoretical Physics, 39, 955, 2000; van der Voorde, A., International Journal of Theoretical Physics, 39, 947–953, 2000; van der Voorde, A., Separation Axioms in Extension Theory for Closure Spaces and Their Relevance to State Property Systems, Doctoral Thesis, Brussels Free University, 2001), and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components for a general state property system (Aerts, D., van der Voorde, A., and Deses, D., Journal of Electrical Engineering, 52, 18–21, 2001; Aerts, D., van der Voorde, A., and Deses, D. International Journal of Theoretical Physics; Aerts, D. and Deses, D., Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation, and Axiomatics, World Scientific, Singapore, 2002). The concept of orthogonality, very important for quantum axiomatics, had however not yet been introduced within the formal scheme of the state property system. In this paper we introduce orthogonality in an operational way, and define ortho state property systems. Birkhoff's well known biorthogonal construction gives rise to an orthoclosure and we study the relation between this orthoclosure and the operational orthogonality that we introduced.     

Nonradiative decay of the low-lying nuclear isomer 229m Th(3.5 eV) in a metal

A new nonradiative decay channel for the anomalously low-lying isomeric level 3/2⁺ (3.5±1.0 eV) of the ²²⁹Th nucleus in a metal via the conduction electrons is examined. The lifetime of the isomer in a metal is calculated. An explanation is given for the experimental results of S. B. Utter et al., Phys. Rev. Lett. 82, 505 (1999), where the optical radiation spectrum of the indicated isomer was investigated. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 367–370 (25 September 1999)     

Crystal structure of ethyl (2Z)-2-(3-methoxy-4-acetyloxy benzylidene)-7-methyl-3-oxo-5-phenyl-2,3-dihydro-5H-[1,3]thiazolo[3,2-a]pyrimidine-6-carboxylate

The title compound, C₂₆H₂₄N₂O₆S, (I), crystallizes in the monoclinic space group, P2₁/c, with cell parameters a = 16.248(1), b = 7.927(1), c = 19.371(4) ?, β = 105.295(2)°, Z = 4. The central pyrimidine ring in the compound (I) is significantly puckered, assuming a screw-boat conformation. The C11–C16 benzene ring stands vertical while thiazole and C18–C23 benzene rings are coplanar to the mean plane of pyrimidine ring having dihedral angles of 87.48(12), 3.63(11) and 0.94(12)°, respectively. In the absence of potential hydrogen bonding interaction, the crystal packing is influenced by intramolecular C-H…S interaction and intermolecular C-H…π interactions.     

Spin exchange and chemi-ionization during collisions of polarized metastable helium atoms with ground-state cesium atoms

The kinetics of the optical orientation of atoms in a helium-cesium gas-discharge plasma are considered, and kinetic equations describing the optical orientation of atoms in the case of two simultaneously occurring processes, viz., an elastic process (spin exchange) and an inelastic process (chemi-ionization), are derived. The rate constants of these processes are determined experimentally: C _se=(2.8±0.8)×10⁻⁹ cm³s⁻¹, C _ci=(1.0±0.3)×10⁻⁹ cm³s⁻¹. Zh. Tekh. Fiz. 69, 36–40 (September 1999)     

Evolution of the structure of Rb2ZnCl4 over the temperature range 4.2–310 K

X-ray diffraction is used to study the temperature dependence of the lattice parameters and the sequence of structural realignments in crystalline Rb₂ZnCl₄ over temperatures of 4.2–310 K. The appearance of and changes in the system of satellite reflexes indicative of structural ordering are studied. Below 74 K, on going into the monoclinic phase (space group A11a), anomalies are observed in the behavior of the lattice parameters, and superstructural reflexes develop with wave vectors q=a ^*/3+b ^*/2+c ^*/2 corresponding to an increase by a large factor in initial parameters a, b, and c of the Pnma-phase. Fiz. Tverd. Tela (St. Petersburg) 41, 1084–1090 (June 1999)     

Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation

The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence. The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found. Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation) is completely solved. Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999)     

Size effect in isometric PbTiO3 crystals

The phase transitions Pm3m⇄P4mm and domain-structure formation in 5–500 μm isometric PbTiO₃ crystals were investigated. The phase transition is characterized by a high rate and by the formation of a single flat interphase boundary {023}. A size effect was observed: In crystals smaller than a critical size (about 20 μm), formation of 90° domains stops and, in agreement with a phenomenological theory, the temperature hysteresis of the phase transition doubles. Fiz. Tverd. Tela (St. Petersburg) 40, 1546–1547 (August 1998)     

On the experimental verification of the Landau-Pomeranchuk-Migdal effect

A theoretical explanation is given for the “unexpected” behavior recently observed in the radiation spectrum of ultrarelativistic electrons in a thin layer of matter in an experimental investigation of the Landau-Pomeranchuk-Migdal effect at SLAC [S. R. Klein et al., Preprint SLAC-6378, Stanford (1993); P. L. Anthony et al., Phys. Rev. Lett. 75, 1949 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 837–840 (10 June 1996)     

Photoelectric properties of ITO/p +-p −-InP solar cells in linearly polarized light

Indium phosphide heterostructures and transparent conducting films of wide-gap oxides have previously been used in the development of highly efficient solar cells, making it possible to bring their efficiencies up to 18% [M. M. Koltun, Optics and Metrology of Solar Cells [in Russian], Nauka, Moscow (1985); V. M. Botnaryuk, L. S. Gagara, L. V. Gorchak et al., Geliotekhnika 23, 37 (1990); V. Botnariuc, L. Gagara, E. Negru et al., Solar Energy in Romania 2(1), 53 (1993)]. In the present paper results are reported from the first studies of the photoelectric properties, in linearly polarized light, of solar cells consisting of a heterojunction between single crystal indium phosphide and a mixed indium and tin oxide film (ITO film, E _g ≅3.6 eV [G. Check and A. Genis, Solid State Techol. 23(1), 102 (1980)]). Zh. Tekh. Fiz. 68, 72–76 (May 1998)     

Main parameters of a coaxial electrostatic lens

Coaxial electrostatic lenses are used in combination with a magnetic field in plasma-optical and manometric devices [A. I. Morozov and S. V. Lebedev, in Reviews of Plasma Physics, Vol. 8, M. A. Leontovich (ed.), Consultants Bureau, New York (1980); V. P. Afanas’ev, A. A. Vydrik, L. P. Ovsyannikova, and E. V. Shpak, Sov. Phys. Tech. Phys. 25, 1049 (1980)]. Their employment in systems for transporting beams of high-energy charged particles is also known [P. Krejcik, B. V. King, and I. C. Kelly, Optik (Stuttgart) 55, 385 (1980)], since, along with quadrupole lenses, they have a large optical strength. Expressions for the trajectories of charged low-energy particles were obtained by L. P. Ovsyannikova and S. V. Pasovets [Sov. Phys. Tech. Phys. 32, 1422 (1987)] in the approximation of a rectangular field model with consideration of the variation of the energy at the entrance and exit from the field. The possibility, in principle, of focusing a parallel beam in a ring is demonstrated. Zh. Tekh. Fiz. 67, 81–82 (December 1997)     

Random-Cluster Representation of the Blume–Capel Model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model. Mathematics Subject Classification (2000): 82B20, 60K35.     

Spontaneous emission in dielectric nanoparticles

An analytical expression is obtained for the radiative-decay rate of an excited optical center in an ellipsoidal dielectric nanoparticle (with sizes much less than the wavelength) surrounded by a dielectric medium. It is found that the ratio of the decay rate A _nano of an excited optical center in the nanoparticle to the decay rate A _bulk of an excited optical center in the bulk sample is independent of the local-field correction and, therefore, of the adopted local-field model. Moreover, the expression implies that the ratio A _nano/A _bulk for oblate and prolate ellipsoids depends strongly on the orientation of the dipole moment of the transition with respect to the ellipsoid axes. In the case of spherical nanoparticles, a formula relating the decay rate A _nano and the dielectric parameters of the nanocomposite and the volumetric content c of these particles in the nanocomposite is derived. This formula reduces to a known expression for spherical nanoparticles in the limit c ≪ 1, while the ratio A _nano/A _bulk approaches unity as c tends to unity. The analysis shows that the approach used in a number of papers {H. P. Christensen, D. R. Gabbe, and H. P. Jenssen, Phys. Rev. B 25, 1467 (1982); R. S. Meltzer, S. P. Feofilov, B. Tissue, and H. B. Yuan, Phys. Rev. B 60, R14012 (1999); R. I. Zakharchenya, A. A. Kaplyanskii, A. B. Kulinkin, et al., Fiz. Tverd. Tela 45, 2104 (2003) [Phys. Solid State 45, 2209 (2003)]; G. Manoj Kumar, D. Narayana Rao, and G. S. Agarwal, Phys. Rev. Lett. 91, 203903 (2003); Chang-Kui Duan, Michael F. Reid, and Zhongqing Wang, Phys. Lett. A 343, 474 (2005); K. Dolgaleva, R. W. Boyd, and P. W. Milonni, J. Opt. Soc. Am. B 24, 516 (2007)}, for which the formula for A _nano is derived merely by substituting the bulk refractive index by the effective refractive index of the nanocomposite must be revised, because the resulting ratio A _nano/A _bulk turns out to depend on the local-field model. The formulas for the emission and absorption cross sections σ_nano for nanoparticles are derived. It is shown that the ratios σ_nano/σ_bulk and A _nano/A _bulk are not equal in general, which can be used to improve the lasing parameters. The experimentally determined and theoretically evaluated decay times of metastable states of dopant rare-earth ions in crystalline YAG and Y₂O₃ nanoparticles are compared with the corresponding values for bulk crystals of the same structure. Original Russian Text ? K.K. Pukhov, T.T. Basiev, Yu.V. Orlovskii, 2008, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 88, No. 1, pp. 14–20.     

Interaction of acoustic and optical branches via a Lifshitz-type invariant

It is shown that the interaction of the acoustic and soft optical branches of the spectrum of normal vibrations of a crystal via a gradient invariant of the Lifshitz-invariant type explains the characteristic temperature dependences of these branches as the point of a transition from the initial phase into an incommensurate phase is approached. A comparison is made with the experimental data for betaine calcium chloride dihydrate — BCCD. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 707–710 (10 May 1997)     

The high-pressure <Emphasis Type="Bold">α/β</Emphasis> phase transition in lead sulphide (PbS)

The high-pressure behaviour of PbS was investigated by angular dispersive X-ray powder diffraction up to pressures of 6.8 GPa. Experiments were accompanied by first principles calculations at the density functional theory level. By combining both methods reliable data for the elastic properties of rock-salt type α- and high-pressure β-PbS could be obtained. β-PbS could be determined to crystallise in the CrB-type (B33), with space group Cmcm. The reversible ferro-elastic α/β transition is of first order. It is accompanied by a large volume discontinuity of about 5% and a coexistence region of the two phases. A gliding mechanism of {001} bilayers along one of the cubic 〈110〉 directions governs the phase transition which can be described in terms of group/subgroup relationships via a common subgroup, despite its reconstructive character. The quadrupling of the primitive unit cell indicates a wave vector (0, 0,π/ a ) on the Δ-line of the Brillouin zone. Received 11 October 2002 Published online 14 February 2003 RID="a" ID="a"Also at: Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16253 Praha 6, Czech Republic e-mail: knorr@min.uni-kiel.de RID="b" ID="b"Present address: University of Cambridge, Cavendish Laboratory (TCM), Madingley Road, Cambridge CB3 0HE, UK RID="c" ID="c"Present address: Johann-Wolfgang Goethe Universit?t, Mineralogisches Institut, Kristallographie, Senckenberganlage 30, D 60054 Frankfurt a.M., Germany     

Ultrafast vibronic phase transitions induced in semiconductors by femtosecond laser pulses

The intermode anharmonic interaction in the theory of ultrafast (t∼10⁻¹³ s) vibronic phase transitions induced on semiconductor surfaces (Si, GaAs) by femtosecond laser pulses is calculated. The conditions for plasma-induced transitions either to a state of chaotic disorder in the positions of the atoms (“cold liquid”) or into a state with crystal symmetry different from the initial symmetry (a new crystalline phase) are determined. It is shown that a NaCl-type structure is realized in GaAs for a transition of the second type, the transition being due to the instability of the longitudinal optical phonon branch. The corresponding numerical estimates are made for Si and GaAs. Fiz. Tverd. Tela (St. Petersburg) 41, 1462–1466 (August 1999)     

Symmetries on Partially Ordered Abelian Groups

Recently, Foulis (Foulis, D. J. (2003). Compressible groups, Mathematica Slovaca 53, 433–455.) characterized compressions on effect rings, which were introduced as a generalization of unital C*-algebras in the context of ordered abelian groups with order units. In the present paper, we characterize a class of symmetries on effect rings and show their relations to compressions. This characterization leads to a generalization of the notion of orthosymmetric orthoposets (Mayet, R., Pulmannová, S. (1994). Nearly orthosymmetric ortholattices and Hilbert spaces, Foundations of Physics 24, 1425–1437.) to symmetric ordered abelian groups with order units.     

Charge ordering in crystals of Pr1? x Sr x MnO3 ( x = 0.22, 0.24) ferromagnetic manganites

The structural and magnetic states of Pr_1−x Sr _x MnO₃ (x = 0.22, 0.24) manganite crystals were studied over a wide temperature range. Measurements of the magnetic susceptibility and electrical resistivity demonstrated that these manganites belong to the class of ferromagnetic semiconductors. Thermal neutron elastic scattering patterns revealed that, in the temperature range 4.2–350 K, the manganites have an orthorhombic structure (space group Pnma) with a well-pronounced cooperative Jahn-Teller effect. Major emphasis was placed on the nuclear magnetic superstructure with a wave vector q = (2π/2a, 0, 2π/2c). It was shown that this superstructure suggests 1/4-type charge ordering in the manganites under investigation. Original Russian Text ? S.F. Dubinin, S.G. Teploukhov, V.E. Arkhipov, V.D. Parkhomenko, é.A. Neĭfel’d, A.V. Korolev, N.A. Ugryumova, Ya.M. Mukovskiĭ, 2007, published in Fizika Tverdogo Tela, 2007, Vol. 49, No. 4, pp. 704–710.     

A theory of the magnetic susceptibility of composites

The absorption of ac magnetic field energy by nonconducting composites made with fillers consisting of microscopic magnetic inclusions with various shapes is investigated over a wide range of frequencies and temperatures. It is predicted that the temperature dependence of the susceptibility χ(ω,T) of these structures is nonstandard only when the interaction between particles of the finely dispersed phase is included. The effect of the magnetic particles is taken into account by introducing a stochastic force into the Boltzmann equation, and using the resulting equation to calculate the susceptibility χ, which is a complicated function of the concentration p of the added dispersed phase. It is shown that the susceptibility should have a singularity near the point p=p _cr. Fiz. Tverd. Tela (St. Petersburg) 39, 1622–1627 (September 1997)     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

Manifestation of ferromagnetism in lightly oxygen-doped La2CuO4 single crystals in magnetic fields H<50 Oe

The temperature and field dependences χ(T,H) in La₂CuO_4+δ single crystals with δ<0.015 have been investigated in magnetic fields 0.1<H<450 Oe by the differential magnetic susceptibility method. It was found that under oxygen doping conditions ferromagnetic regions are formed. These regions produce a characteristic curve of the magnetic susceptibility χ(T,H), which is observed only in magnetic fields of less than 50 Oe. This can be explained by the formation of ferrons [A. Aharony et al. Phys. Rev. Lett. 60, 1330 (1988); L. I. Glazman and A. S. Ioselevich, Z. Phys. B 80, 268 (1990)] in an antiferromagnetic matrix. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 152–155 (10 August 1996)