Neutron diffraction studies of the premartensitic transformation B2 → B19′ in Ti49Ni51 single crystals

We have studied structural changes in the high-temperature B2-phase in a large single crystal at temperatures near the premartensitic transformation B2 B19. We are the first to observe an extra 1/2 (110) reflection in neutron diffraction patterns taken along the [110]_B2 direction as the sample is cooled below 420 K, but still far from the martensite start temperature (M_s=180 K). This extra reflection heralds the formation of long-range order in atomic displacements with wave vectorq=(1/2±)[110]2/a. Premartensitic diffraction effects (caused by the development and correlation of lattice waves of atomic displacements with wave vectorsq ₁2/a[1/3, 1/3, 0] andq ₁2/1[1/3, 1/3] that were clearly visible in this same single crystal before the martensitic transformation B2 R, appeared at even lower temperatures with substantially lower intensities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 56–61, January, 1995.     

Correlation functions and pressure of a nonisothermal plasma

Expressions are obtained for the correlation functions of a classical nonisothermal two-component plasma. In the limiting case _{e i} strong correlations arise because of the presence of weakly-damped waves (ion acoustic waves) with a phase velocity lying between the thermal velocities of the particles u_e /k u_i. Under such conditions the correction to the pressure because of Coulomb interaction changes sign in comparison with the case of thermodynamic equilibrium, when there are no such waves.     

Probability distribution of internal distances of a single polymer in good solvent

IfP _ij(x) is the probability distribution function of the scaled distancex between two elementsi andj of a long polymer in a good solvent, it is shown by Monte Carlo calculations that is in good agreement with out data for allx (B is a normalization constant). As a model we consider the freely jointed chain consisting ofN=160 rigid links. We estimate the exponents to ₀=0.27±0.01, ₀=2.44±0.02 (fori=1,j=N); ₁=0.55±0.06, ₁=2.60±0.15 (fori=1,j=N/2); ₂=0.9±0.1, ₂=2.48±0.06 (fori=N/4,j=3N/4). ₀ and ₀ are in agreement with ₀=1/(1-v) and ₀=(-1)/v proposed by Fisher and des Cloiseaux respectively, but we find concerning ₁ and ₂ that our estimates differ from recent -expansion calculations, by an amount of 20–30%. We analyse the crossover between the various exponents.     

Do quasiparticles in high-Tc superconductors condense like molecules of a perfect gas in the bose-Einstein condensation?

Far IR transmission spectra of very thin YBaCuO films in the 10–40 cm^–1 range have now sufficient accuracy and reproducibility to show that the number of quasiparticles at temperature <_c, _c being the transition temperature, do not follow a ⁴ law, but rather a ^1.5 one.     

Thermal atomic vibrations in Cu-Ni alloys

Copper radiation has been used in an x-ray study of the temperature dependence of the effective characteristic x-ray temperature _p(T) for the alloys of the Cu-Ni system over the temperature range 293–1073 °K and in a determination of the concentration dependence of d ln_p/dT for the alloys. It is shown that _p(c) is additive. The concentration dependence of d ln_p/dT is linear. The agreement between the experimental results and data in the literature is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 75–80, September, 1970.     

Lyapunov Modes of Two-Dimensional Many-Body Systems; Soft Disks, Hard Disks, and Rotors

The dynamical instability of many-body systems can best be characterized through the local Lyapunov spectrum {}, its associated eigenvectors {}, and the time-averaged spectrum {}. Each local Lyapunov exponent describes the degree of instability associated with a well-defined direction—given by the associated unit vector —in the full many-body phase space. For a variety of hard-particle systems it is by now well-established that several of the vectors, all with relatively-small values of the time-averaged exponent , correspond to quite well-defined long-wavelength modes. We investigate soft particles from the same viewpoint here, and find no convincing evidence for corresponding modes. The situation is similar—no firm evidence for modes—in a simple two-dimensional lattice-rotor model. We believe that these differences are related to the form of the time-averaged Lyapunov spectrum near =0.     

On the measurement of electronic spin-scattering anisotropy in the presence of magnetic interaction effects, using the dHvA Waveshape Analysis method

We derive an expression for the harmonic content of the oscillatory magnetization (de Haas-van Alphen effect) which is valid in the most general case, when the harmonic amplitudes and the relative harmonic phases of the pure Lifshitz-Kosevitch (LK) theory are modified by an arbitrary combination of magnetic interaction (MI), spin-scattering anisotropy (SSA) and exchange shift effects. The calculation produces several conclusions which bear directly upon the possibility of generally being able to determine separately the up-spin and down-spin conduction electron lifetimes in the presence of magnetic impurities, by means of measurements of the amplitudes and relative phase of the fundamental and second harmonic dHvA oscillations. We have shown that not only does SSA shift the first and second LK harmonics in phase, by amounts₁ and₂, but SSA also shifts the second harmonic magnetic interaction component by an amount 2₁. We find that, in general, the combined effect of both MI and SSA on the observable relative phase angle, (2 ₁–₂), can either add or cancel. In the limit in which the second harmonic is dominated by the MI component it can be shown that (2 ₁–₂) goes to , regardless of the amount of SSA, so that no useful information regarding SSA can be obtained from (2 ₁–₂) in this case. Measurable quantities and measurement techniques, for the determination of SSA, are discussed briefly.Research conducted at the University of Oregon with support from the National Science Foundation (USA).     

High-temperature resistivity of Ti1-X Al X alloys

We have measured the high-temperature resistivities of dilute Ti_1-x Al _x alloys withx0.135 up to 1100 K (2.6 _D , where _D is the Debye temperature). We observe that possesses a strong downward deviation from a linear temperature-dependence at high temperatures (several hundred degrees Kelvin). Eventually, saturates to a constant. This non-Bloch-Grüneisen-like behavior is compared with the predictions of current theories.     

Antiferromagnetic-paramagnetic transition in AlCr2

Measurements have been made on the AF P magnetic phase transition in AlCr₂, which has a Cll_b superlattice. The transition is affected by ordering and a structural transformation. High-temperature calorimetry and x-ray diffraction indicate the transition type. There are anomalies in _p and C_p as well as in the thermal-expansion coefficients as the transition point is approached.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 9–12, April, 1988.     

C*-dynamical systems that are asymptotically highly anticommutative

It is shown that with probability 1 on , resp. ongx the irrational rotation algebra with respect to the CAT map and the generalized Price-Powers shiftA _X are asymptotically highly anticommutative.     

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

A new theory on scattering of electrons due to spiral dislocations

The topologically singular lattice structure around a spiral dislocation scatters electrons in a manner much different from the deformation-potential-scattering. Thet-matrix is represented ast(k, k)=t ₀ sin (k _z/2) exp (±i _kk/2)/sin ( _kk/2) with the scattering angle _kk, the componentk _z of the wave vector parallel to the dislocation, andt ₀(Fermi energy). This kind of scattering alone does not cause a perpendicular resistivity, but in a dirty limit a specific dislocation resistivity does exist, whose relaxation time per unit length of dislocation is of the order of/(Fermi energy).Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-KölnOn leave of absence from Department of Materials Science, Hiroshima University, Higashisenda-machi, Hiroshima, Japan     

Magnetic properties of solid solutions of the system ErxY1−xFe2

The magnetic properties of the system Er_xY_1–xFe₂ (MgCu₂ structure) in the temperature range 80–800°K are investigated. The magnetization and the coercive force H_c are measured as a function of T. For alloys with x= 0.5–1 there is a magnetic compensation point _c. The composition dependence of _c, the magnetic moment of the alloy and of the iron atoms Fe are determined. An H_c anomaly is observed in _c. In order to explain the results obtained, the presence of two types of magnetically active atoms and three types of exchange interaction are included.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 10, pp. 27–30, October, 1982.     

Boundary critical behavior ofd=2 self-avoiding walks on correlated and uncorrelated vacancies

In this paper we present exact results for the critical exponents of interacting self-avoiding walks with ends at a linear boundary. Effective interactions are mediated by vacancies, correlated and uncorrelated, on the dual lattice. By choosing different boundary conditions, several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the model. In particular, the problem of boundary exponents at the -point is fully solved, and implications for-point universality are discussed. The surface crossover exponent at the special transition of noninteracting self-avoiding walks is also interpreted in terms of percolation dimensions.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

R-Operator, Co-Product and Haar-Measure for the Modular Double of

A certain class of unitary representations of U_q((2,)) has the property of being simultanenously a representation of for a particular choice of (q). Faddeev has proposed to unify the quantum groups U_q((2,)) and into some enlarged object for which he has coined the name ``modular double'. We study the R-operator, the co-product and the Haar-measure for the modular double of U_q((2,)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.     

Influence of Nonplanar Distortions of the Tetrapyrrole Macroring on the Electronic States of the Tetraphenylporphin Dication

Quantum-chemical calculations of the electronic structure of the tetraphenylporphin dication have been made by the CNDO/S method for various values of the parameter of saddle-like distortions of the porphyrin macroring of angle and the dihedral angle between the macroring planes and the phenyl rings. It is shown that the boundary highest occupied molecular orbital (HOMO) of symmetry a _2u is the most sensitive to variations in and and its order can be changed relative to another HOMO of symmetry a _1u . The behavior of the lower excited electronic singlet and triplet states depending on and has been analyzed in detail. In particular, the addition of configurations with charge transfer to the Q, B, and N states as well as to the T ₁ and T ₂ states has been determined quantitatively. An interpretation of the experimental spectra of porphyrin dications on the basis of the calculation results is given.     

Noncommutative Cohomology and Electromagnetism on $$\mathbb{C}$$ q [SL2] at Roots of Unity

We compute the noncommutative de Rham cohomology for the finite dimensional q-deformed coordinate ring _q [SL₂] at odd roots of unity and with its standard four-dimensional differential structure. We find that H ⁱ is highly nontrivial compared to case of generic q and has as many modes 1 : 4 : 6 : 4 : 1 as the dimension of the exterior algebra. We solve the spin-0 and Maxwell theory on _q [SL₂], including a complete picture of the self-dual and anti-self dual solutions and of Lorentz and temporal gauge fixing. The system behaves in fact like a noncompact space with self-propagating modes (i.e., in the absence of sources). We also solve with examples of electric and magnetic sources including the biinvariant element H ¹ which we find can be viewed as a source in the local (Minkowski) time-direction (i.e. a uniform electric charge density).     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.