State Property Systems and Closure Spaces: A Study of Categorical Equivalence

We show that the natural mathematical structureto describe a physical entity by means of its states andits properties within the Geneva–Brussels approachis that of a state property system. We prove that the category of state property systems (andmorphisms) SP is equivalent to the category ofclosure spaces (and continuous maps) Cls. We showthe equivalence of the state determinationaxiom for state property systems with the T₀separation axiom for closure spaces. We alsoprove that the category SP ₀ ofstate-determined state property systems is equivalent tothe category L ₀ of based completelattices. In this sense the equivalence of SP andCls generalizes the equivalence ofCls ₀ (T₀ closure spaces)and L ₀ proven by Erne(1984).     

T0 Separation in Axiomatic Quantum Mechanics

Using the physical duality between states and properties, Aerts et al. obtained alattice representation for all closure spaces, through state property systems. Inthis paper I discuss the equivalence of 'state determination' for state propertysystems with T₀ separation for closure spaces. I also provide a link withwell-known lattice representations of closure spaces, through some results of Erné.     

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.     

Evidence of maximum in the melting curve of hydrogen at megabar pressures

Hydrogen at high pressures of ∼400 GPa might be in a zero-temperature liquid ground state (N. Ashcroft, J. Phys.: Condens. Matter A 12, 129 (2000), E. G. Brovrnan et al., Sov. Phys. JETP 35, 783 (1972)). If metallic hydrogen is liquid, the melting T _melt(P) line should possess a maximum. Here we report on the experimental evaluation of the melting curve of hydrogen in the megabar pressure range. The melting curve of hydrogen has been shown to reach a maximum with T _melt = 1050 ± 60 K at P = 106 GPa and the melting temperature of hydrogen decreases at higher pressures so that T _melt = 880 ± 50 K at P = 146 GPa. The data were acquired with the aid of a laser heating technique where diamond anvils were not deteriorated by the hot hydrogen. Our experimental observations are in agreement with the theoretical prediction of unusual behavior of the melted hydrogen [S. Bonev et al., Nature 481, 669 (2004)]. The article is published in the original.     

Coexistence of superfluid and solid helium in aerogel

The results of recent neutron scattering studies of solid helium in silica aerogel are discussed. Previously I.V. Kalinin et al., Pis’ma Zh. éksp. Teor. Fiz. 87 (1), 743 (2008) [JETP Lett. 87 (1), 645 (2008)], we detected the existence of a superfluid phase in solid helium at a temperature below 0.6 K and a pressure of 51 bar, although, according to the phase diagram, helium should be in the solid state under these conditions. This work is a continuation of the above studies whose main goal was to examine the detected phenomenon and to establish basic parameters of the existence of a superfluid phase. We have determined the temperature of the superfluid transition from solid to superfluid helium, T _C = 1.3 K, by analyzing experimental data. The superfluid phase excitation parameters (lifetime, intensity, and energy) have a temperature dependence similar to that of bulk helium. The superfluid phase coexists with the solid phase in the entire measured temperature range from T = 0.05 K to T _C and is a nonequilibrium one and disappears at T _C.     

Neutron scattering study of transverse magnetism in the metamagnet FeBr2

In order to clarify the nature of the additional phase transition at H ₁ ( T ) < H _c ( T ) of the layered antiferromagnetic (AF) insulator FeBr ₂ as found by Aruga Katori et al. (1996) we measured the intensity of different Bragg-peaks in different scattering geometries. Transverse AF ordering is observed in both AF phases, AF I and AF II. Its order parameter exhibits a peak at T ₁ = T ( H ₁ ) in temperature scans and does not vanish in zero field. Possible origins of the step-like increase of the transverse ferromagnetic ordering induced by a weak in-plane field component when entering AF I below T₁ are discussed. Received 27 September 1999 and Received in final form 6 December 1999     

Microscopic interactions in CuGeO 3 and organic Spin-Peierls systems deduced from their pretransitional lattice fluctuations

CuGeO₃ exhibits a Spin-Peierls (SP) transition, at T _SP = 14.3 K, which is announced above 19 K by an important regime of one-dimensional (1D) pretransitional lattice fluctuations which can be detected until about 40 K using X-ray diffuse scattering investigations. A quantitative analysis of this scattering shows that in this 1D direction the correlation length follows the “universal” behaviour expected for the thermal fluctuations of a real order parameter which characterizes the lattice dimerization. This allows to define a 1D mean-field temperature, T _SP ^MF , of about 60 K and invalidates any mean field scenario for the SP transition of CuGeO₃. As T _SP ^MF is as high as 4 T _SP we propose that the 3D-SP order is achieved by the interchain coupling between 1D solitons which form below about 16-20 K. CuGeO₃ being in the non-adiabatic regime, it is also suggested that the observed pretransitional fluctuations of CuGeO₃ originate from the X-ray scattering on a very broad damped critical response of lower frequency than the “critical” phonon modes. From the quantitative analysis of the 1D fluctuations we also estimate the microscopic parameters of the SP chain. These parameters allow to locate CuGeO₃ close to the quantum critical boundary separating the gapped SP ground state to the ungapped anti-ferromagnetic ground state. The vicinity of a quantum critical point emphasizes the role of the quantum and non-adiabatic fluctuations and the importance of the interchain coupling in the physics of CuGeO₃. Finally we compare these findings with those obtained for the organic SP systems (BCPTTF)₂PF₆, (TMTTF)₂PF₆ and MEM(TCNQ)₂. From a similar analysis of the pretransitional lattice fluctuations it is found that (BCPTTF)₂PF₆ and (TMTTF)₂PF₆ are located on the SP gapped classical-quantum boundary and are in the adiabatic regime where the fluctuations lead to the formation of a pseudo-gap in the spin degrees of freedom. Differently, we place MEM(TCNQ)₂ inside the SP quantum phase around the crossover line between the adiabatic and non-adiabatic regimes. Received 13 September 2000 and Received in final form 6 February 2001     

<Emphasis Type="Italic">Comment on</Emphasis>¶Low temperature specific heat of blue bronze K <Emphasis Type="Bold">0.30</Emphasis>MoO <Emphasis Type="Bold">3</Emphasis>, by J. Odin,J.C. Lasjaunias,K. Biljaković, K. Hasselbach,and P. Monceau

Eur. Phys. J. B 24, 315 (2001) Here we comment on a recently published paper on the presence of a phason contribution in the low temperature heat capacity data of the charge-density-wave compounds K_0.3MoO₃ and (TaSe₄)₂I. We have shown that the anomaly in the C _P / T ³ data reported by Odin et al. is straightforwardly interpreted in terms of low energy phonon modes resulting from the peculiar topology of these compounds. Received 21 February 2002 Published online 19 July 2002     

Path integral approach for superintegrable potentials on spaces of non-constant curvature: II. Darboux spaces <Emphasis Type="Italic">D</Emphasis><Subscript>III</Subscript> and <Emphasis Type="Italic">D</Emphasis><Subscript>IV</Subscript>

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze five and four superintegrable potentials in the spaces D _III and D _IV, respectively; these potentials were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green’s functions, the discrete and continuous wavefunctions, and the discrete energy spectra. In some cases, however, the discrete spectrum cannot be stated explicitly because it is determined by a higher-order polynomial equation. We also show that the free motion in a Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We can state the corresponding energy spectrum and the wavefunctions. The text was submitted by the authors in English.     

Scheme for implementing perfect quantum teleportation with four-qubit entangled states in cavity quantum electrodynamics

Recently, Peng et al. [2010 Eur. Phys. J. D 58 403] proposed to teleport an arbitrary two-qubit state with a family of four-qubit entangled states, which simultaneously include the tensor product of two Bell states, linear cluster state and Dicke-class state. This paper proposes to implement their scheme in cavity quantum electrodynamics and then presents a new family of four-qubit entangled state |Ω₄>₁₂₃₄. It simultaneously includes all the well-known four-qubit entangled states which can be used to teleport an arbitrary two-qubit state. The distinct advantage of the scheme is that it only needs a single setup to prepare the whole family of four-qubit entangled states, which will be very convenient for experimental realization. After discussing the experimental condition in detail, we show the scheme may be feasible based on present technology in cavity quantum electrodynamics.     

Comment on the paper “Nature of low-temperature phase transitions in CaMn7O12”

We contend that the anomalies observed in the magnetization, specific heat, and thermal expansion of CaMn₇O₁₂ at T _S = 89 K and T _M = 49 K reported in O. Volkova et al., Pis’ma v ZhETF 82, 498 (2005) [JETP Lett. 82, 444 (2005)] and mentioned in Pis’ma v ZhETF 82, 724 (2005) [JETP Lett. 82, 642 (2005)] are both of magnetic origin. The text was submitted by the authors in English.     

The topology of homophase misorientation spaces

Homophase misorientation spaces are investigated with a focus on the effect of symmetry operations on their topology and their minimum embedding dimensions in Euclidean space. Whereas the topology of rotation space is well established and requires a minimum of five variables for a one-to-one and continuous mapping, the spaces of orientations and misorientations are quotient spaces of the rotation space and are obtained by applying various equivalence relations. The equivalence relations for orientation spaces only involve the rotational symmetries of the underlying crystals. These spaces are classified under the three-dimensional manifolds called the spherical 3-manifolds, which have a non-trivial fundamental group, are not simply connected spaces, and do not embed in three-dimensional Euclidean space. In the case of homophase misorientation spaces, however, in addition to rotational symmetry operations there is a further ‘grain exchange symmetry’, which is shown to simplify the topology considerably. In some important cases this symmetry also reduces the number of Euclidean dimensions required to embed these misorientation spaces. The homophase misorientation spaces for the dihedral point groups D ₂(222), D ₄(422) and D ₆(622), the tetrahedral point group T(23), and the octahedral group O(432) are all found to be embeddable in only three dimensions, two dimensions less than required for rotations. Hence, these misorientation systems can be represented using three variables in a one-to-one and continuous manner.     

Thermodynamic properties of the spin-Peierls transition in CuGeO3

We present an investigation of the spin-Peierls transition atT _SP=14.5 K in polycrystalline CuGeO₃ through specific-heat and thermal-expansion measurements. Clear second-order phase-transition anomalies are found in both properties atT _SP, although only a small entropy of S0.1 Rn2 is released at the transition. Most of the entropy is released atT _SP<T<150 K, where the temperature dependence of the magnetic contribution to the specific heat as well as the thermal expansion exhibit extrema atT ^*40 K. These are caused by one-dimensional antiferromagnetic fluctuations along the Cu chains, possibly accompanied by structural fluctuations. Using Ehrenfest's relation, a hydrostatic pressure coefficient (T _SP/_p)_p0 (0.45±0.06) K/kbar is derived.     

ESR millimeter-band spectroscopy of magnetic ordering in the low-dimensional magnet CuGeO3

Resonant absorption of microwaves in CuGeO₃ single crystals in a frequency band of 40 to 120 GHz, in magnetic field B⩽15 T, at temperatures ranging between 0.5 and 300 K, and in the configuration B∥a has been investigated. Several absorption lines (S ₀, S _a, and S _b) whose parameters strongly depend on temperature have been detected close to ESR. The temperature dependence of the total absorption in the main line S ₀ with the Landé g-factor g ₀=2.154 at temperatures above the spin-Peierls transition temperature is in good agreement with Bonner and Fisher’s theoretical prediction for a one-dimensional Heisenberg spin chain. In addition to the main resonance, a resonance of smaller amplitude, S _a, with the g-factor g _a=2.72 has been detected at temperatures ranging down to a characteristic temperature T≃1 K, below which the amplitude of this feature drops to zero. A radical restructuring of the magnetoabsorption spectrum occurs at the temperature of the spin-Peierls transition T _SP≈14 K. At T<12 K new features emerge in the spectrum, namely, a broad absorption line overlapping with the narrow lines S ₀ and S _a, and a line S _b with g _b=1.83, which is not detected at temperatures above T _SP. An analysis of amplitudes and total absorption of ESR lines as functions of temperature has shown that the temperature range below 1 K is anomalous, which may be caused by an additional ordering in the CuGeO₃ magnetic subsystem at low temperatures. Zh. éksp. Teor. Fiz. 112, 1727–1738 (November 1997)     

Nonmonotonic behavior of magnetoresistance, R(H) hysteresis, and low-temperature heat capacity of the BaPb0.75Bi0.25O3 superconductor in a magnetic field: Possible manifestations of phase separation

The transport properties (R(T) and R(H) dependences at various values of the transport current in magnetic fields up to 65 kOe) and low-temperature heat capacity in magnetic fields up to 90 kOe of the BaPb_0.75Bi_0.25O₃ superconductor (T _C ≈ 11.3 K) are investigated with the goal of clarifying the mechanisms determining the nonmonotonic behavior and hysteresis of its magnetoresistance R(H). The type of R(H) hysteretic dependences for BaPb_0.75Bi_0.25O₃ is analogous to that observed in granular high-T _c superconductors (HTSCs); however, unlike classical HTSC systems, the field width of the magnetoresistance hysteresis loop for polycrystalline BaPb_0.75Bi_0.25O₃ depends on the transport current. This means that although the mechanisms responsible for the magnetoresistance hysteresis (the influence of the magnetic flux trapped in superconducting regions on the effective field in Josephson interlayers) are identical in these objects, the transport current in BaPb_0.75Bi_0.25O₃ may considerably affect the diamagnetic response of the superconductor. A considerable effect of transport current on the field in which the R(H) dependences have a peak and exhibit hysterestic properties is observed. Such a behavior can be adequately interpreted using the model of the spatially inhomogeneous superconductor-insulator state proposed by Gorbatsevich et al. [JETP Lett. 52, 95 (1990)]. The nonmonotonic dependence of quantity C/T (C is the heat capacity) on the magnetic field discovered in the present study also agrees with the conclusions based on this model.     

The lowest electronic states of Ne2 +, Ar2 + and Kr2 +: comparison of theory and experiment

Non-relativistic configuration interaction (CI) ab initio calculations using large basis sets have been carried out to determine the potential curves of the first electronic states of Ne₂ ⁺, Ar₂ ⁺ and Kr₂ ⁺. The spin—orbit interaction was treated assuming that the spin—orbit coupling constant is independent of the internuclear separation (R). For Ar₂ ⁺, calculated dissociation energies and equilibrium separations are in good agreement with experimental results. The calculations for Ne₂ ⁺ suggest that the lowest vibrational level of the I(1/2u) ground state observed by threshold photoelectron spectroscopy by Hall et al. [1995, J. Phys. B: At. molec. opt. Phys., 28, 2435] and assigned to either ν = 0 or ν = 2 actually corresponds to ν = 4. The calculations also predict the I(1/2g) state of Ne₂ ⁺ and Ar₂ ⁺ to possess a double-well potential and that of Kr₂ ⁺ to be repulsive at short range and to only possess a single shallow well at large internuclear separation. The ab initio calculations provide an explanation for the observation made by Yoshii et al. [2002, J. chem. Phys., 117, 1517] that Kr₂ ⁺ and Xe₂ ⁺ dissociate after photoemission from the II(1/2u) state to the I(1/2g) state whereas Ar₂ ⁺ does not.     

Anomalous Ortho-to-Para Ratio of Nuclear Spin Isomers of H2O at Low Temperatures

A theoretical model proposed for nuclear spin isomers of H₂O molecules located inside the C₆₀ fullerene explains an anomalously high stability of ortho-H₂O isomers detected in the experiments reported in [B. Meier et al., Nature Commun. 6, 8112 (2015)] at a temperature of T = 5 K.

     

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)     

Pressure,temperature and light influence on spin transition solids

Abstract

Present paper is an overview of our efforts during the past few years to understand complicated corelations of physical phenomena related to pressure in Fe(I1) solid state spin transition systems. Some principal results concerning p, T, λ-experiments are extracted. In the context of correlation of the crystallographic phase transition with simultaneous HS → LS relaxation and LS → HS photopopulation, we show the latest results: Brillouin and magnetic measurements on the crystal [Fe(pt₆](BF₆)₂.