Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

Effect of bias field on the dielectric properties of 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 single crystals with different orientations

Microdomain-macrodomain transformations and phase transitions in 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ single crystals were investigated by studying their relative permittivity under various dc bias at constant heating and cooling rates. The orientation dependence of the bias field effect was revealed by examining the temperature dependence of relative permittivity as a function of crystal orientation (the 111, 011 and 001 directions) and dc bias field. The crystals have a microdomain rhombohedral ferroelectric state in the ferroelectric phase under zero dc bias. External bias field could modulate the domain state and induce a macrodomain state in the crystals. Also, it is proposed that the dc bias applied along the 001 or 011 direction could induce a tetragonal ferroelectric phase or an orthorhombic ferroelectric phase, respectively, in an intermediate temperature range. PACS 77.80.-e; 77.22.-d; 81.40.-z     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

Improved bounds for the transition temperature of directed polymers in a finite-dimensional random medium

We consider the problem of directed polymers in a random medium of a finitedimensional lattice. In the high-temperature phase of this system it is known that the annealed and quenched free energies coincide. Upper bounds on the transition temperature to a low-temperature phase had previously been obtained by calculating the first two moments Z and Z² of the partition function. We improve these bounds by estimating noninteger moments Z for 1<<2.     

On the zigzagging causility model of EPR correlations and on the interpretation of quantum mechanics

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B B|. An exact correspondence exists between the Born-Jordan-Dirac wavelike algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (B| were over real hidden states. While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes A|C = C|A*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |A|C|². CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is | U | = | U = U|, with | denoting a preparation, | a measurement, and U the evolution operator. The transformation | = |U or | = |U^–1 exchanges the preparation representation and the measurement representation of a system and is ancillary in the formalization of the quantum chance game by the wavelike algebra of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude A|C = A|BB|C between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility A|C = C|A* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of blind statistical retrodiction—that is, of final cause.Dedicated to Professor David Bohm, proponent of the EPRB version of nonseparability.     

Renormalized transport equations for the bistable potential model

Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value x _t can be evaluated in both domains Dx _± and xD ₀ outside and between the potential minima, leading to drastic differences of the dynamics prevailing inD _± andD ₀, respectively.     

Molecular dynamics study of nematic liquid crystal orientation ordering

Molecular dynamics investigations of distribution functions of orientation, order parameters P ₂, P ₄ and selfdiffusion tensor components for nematic liquid crystal model were performed. Our results are in good agreement with experimental data for p-azoxyanisole (PAA). Applied molecular dynamics model is perspective for investigations of structure characteristics and transport coefficients of nematic phase.     

The lattice deformation and the energy of antiphase boundaries in Fe-Si alloys

The lattice deformation across the antiphase boundary and the energy of both types (a/2111 anda(100) of antiphase boundaries lying in {110} plane are calculated using a series of three interatomic potentials fitted to experimental data. It is shown that the relaxation of atomic planes in the vicinity of antiphase boundary is important for thea/2111 antiphase boundary and is negligible for a 100 antiphase boundary in the DO₃ structure.The author is grateful to Dr. F.Kroupa and to Dr. A.Gemperle for valuable discussions.     

Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Absence of asymptotic-time symmetry breaking in zero-bias spin-boson model with partial relaxation

The symmetric spin-boson model without external field is treated for any type of coupling to the boson bath and any initial bath density matrix. With initially fully aligned spin (_z (0)= =1), the proof is given that a partial relaxation (_z (+) t1<) implies that there is no asymptotic-time (up-and-down) symmetry breaking (i.e. that _z (+)=0). For the problem of a particle (interacting with free bosons) in a symmetric double well without spatial symmetry breaking before the infinite time limit, this means that att + the particle distribution becomes symmetric (irrespective of the full initial asymmetry) unless the particle fully remains (att + ) in Ihe starting well.     

One-dimensional site percolation on a finite lattice

The behaviour of the numbers n _s of clusters withs sites each in the case of a chain ofN sites is studied for free and cyclic boundary conditions. Explicit expressions for the n _s, which differ from (1–p)² p ^s=q ² p ^s for the infinite lattice, are given. Also the total numberG(p) of clusters and the mean cluster sizeS(p) are calculated. In the thermodynamic limit the correction terms are found to be of order 1/N. An investigation of the scaling behaviour shows that the scaling of n _s is described by two independent variables in contrast toG(p) andS(p) which require only one variable.     

Dynamics of the one dimensional randomly dilute Ising ferromagnet

The effect of randomly dilute impurities in the percolation limit on the relaxation of magnetization M(t) and on the way the time-dependent correlation function M(t)M(0) decays in a one dimensional Ising ferromagnet is considered, as is the behaviour of the dynamic susceptibility. It is found that the decay of the magnetization is hardly altered except for small faster decaying boundary effects. However, the correlation function is drastically altered, decaying in general faster asymptotically than the pure system. The dynamical susceptibility also changes, showing a breaking in the simple relaxational scaling form of the pure system. Crossover behaviour with non-critical slowing down (apart from the critical slowing down asTT _c=0) is also observed in the transition from the pure ferromagnetic to randomly dilute behaviour.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Atomic in-plane disorder in Co/Pt superlattices

We have studied 111 and 001 oriented Co(3 Å)/Pt(18 Å) superlattices grown by molecular beam epitaxy via X-ray diffraction using synchrotron radiation. The diffraction peak shapes, for the scattering vector Q parallel to the film planes, were found to be characteristically different between these two films. For the 111 oriented sample, this broadening is characterized by a Lorentzian peak shape with a positional correlation length of the order of 50 Å. The data further indicate that the atomic correlation in the 111 sample has a long range orientational but only short range positional order.     

Scaling function for the energy density correlation at large momentum

The static energy-density correlation function S ²(0)S ²(x)–S ²² is calculated in the critical region for theS ⁴ Ginzburg-Landau-Wilson model at short distances and for nonzero field. Short distance expansion is used and its structure for more complex vertex functions is given. Goldstone mode singularities present at the magnetization curve are taken into account. The main application is given in the theory of polymer solutions. Here, S ²(0)S ²(x)–S ²² becomes the Fourier transform of the densitydensity correlation.     

Ultra-high piezoelectric response in 〈<Emphasis Type="Bold">110</Emphasis>〉- oriented polydomain Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>- PbTiO<Subscript>3</Subscript> single crystals

The piezoelectric constant and electromechanical coupling coefficients of 110-oriented polydomain0.71Pb(Mg_1/3Nb_2/3)O₃-0.29PbTiO₃ single crystals were determined experimentally by using resonance methods. It was confirmed that the single-crystal system has large electromechanical coupling coefficients k₃₃ (91%), k₃₃ (83%), and k₃₁ (81%), and piezoelectric constant d₃₃ (1400 pC/N), which are comparable to those of 001-oriented crystals, and we also found that the values of k₃₃ and k₃₁ are sensitive to the cuts of the crystals. X-ray-diffraction measurements on 110-oriented crystals have shown that the origin of the high piezoelectric response should be attributed to the orthorhombic distortion. Our results show that the 110-oriented crystals are also promising for a wide range of electromechanical transducer applications, since the 110-oriented crystals can be grown from 110-oriented seed crystals in the modified Bridgman technique. PACS 77.80.Bh; 77.84.Dy; 77.65.Bn     

Random walk with persistence

The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)= _n=0 s ⁿ P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R ²(n), R ⁴(n), and R ⁶(n) are calculated and approximate results forP(R,n) and R ^–1(n) are given.