An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

The modified Korteweg-de Vries equation on the quarter plane with t-periodic data

We study the modified Korteweg-de Vries equation posed on the quarter plane with asymptotically t-periodic Dirichlet boundary datum u(0,t) in the sense that u(0,t) tends to a periodic function g?₀ (t) with period τ as t → ∞. We consider the perturbative expansion of the solution in a small ε > 0. Here we show that if the unknown boundary data u_x(0,t) and u_xx(0,t) are asymptotically t-periodic with period τ which tend to the functions g?₁ (t) and g?₂ (t) as t → ∞, respectively, then the periodic functions g?₁ (t) and g?₂ (t) can be uniquely determined in terms of the function g?₀ (t). Furthermore, we characterize the Fourier coefficients of g?₁ (t) and g?₂ (t) to all orders in the perturbative expansion by solving an infinite system of algebraic equations. As an illustrative example, we consider the case of a sine-wave as Dirichlet datum and we explicitly determine the coefficients for large t up to the third order in the perturbative expansion.     

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L _I (x;λ), with λ a generic coupling constant, such that the following expression ∂ L _I (x;λ)/∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.     

Analysis of temperature and concentration dependence of flow stress in KCl–KBr single crystals with special reference to solute distribution

Available data on the temperature and concentration dependence of critical resolved shear stress (CRSS) of KCl–KBr solid-solution crystals containing 9, 17, 27 and 45?mol% KBr in the temperature range 77–230?K have been analyzed within the framework of the kink-pair nucleation model of plastic flow in solid- solution crystals. It is found that CRSS τ decreases with increasing temperature T in accordance with the model relation lnτ?=?A???BT, where A and B are positive constants. The CRSS τ at a given temperature depends on solute concentration c as τ?∝?c^p , where exponent p has a value between 0.33 and 0.57 as temperature T rises from 0 to 230?K. The model parameter W _o, i.e. binding energy between the edge-dislocation segment L _o involved in the unit activation process and the solute atoms close to it (T?→?0?K), which is inversely proportional to B, increases with solute concentration c monotonically as W _o?∝?c ^0.33 up to a critical value c _m?=?35?mol% KBr, which is in reasonable agreement with the model prediction W _o?∝?c ^0.25. However, W _o decreases with an increase in c beyond c _m, which indicates somewhat ordered distribution of solute in the host lattice of concentrated KCl–KBr solid solutions with c?>?c _m.     

On the range of validity of a semiclassical relation between the critical exponents at the Anderson localization transition

Using Wegner's result relating critical exponents s and ν for conductivity and localization length, respectively, via dimensionality d and that for ν given by García-García, we derive what we term a semiclassical (sc) relation for ν in terms of s, which is independent of dimensionality. Forming the ratio s/ν versus d from the above relations, s/ν=0 at d=2 is due to a singularity in the sc relation for ν. We argue that, in reality, s/ν=0 results from s being zero at d=2. Finally we conjecture that (i) Wegner's prediction s/ν=1 when d=3 and (ii) ν tends to 1/2 at large s, are both insensitive to interactions.     

Solutions of Doubly and Higher Order Iterated Equations

Michael Fisher once studied the solution of the equation f(f(x))=x ²–2. We offer solutions to the general equation f(f(x))=h(x) in the form f(x)=g(ag ^–1(x)) where a is in general a complex number. This leads to solving duplication formulas for g(x). For the case h(x)=x ²–2, the solution is readily found, while the h(x)=x ²+2 case is challenging. The solution to these types of equations can be related to differential equations.     

Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field (B), a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters J_{x=Jy≠Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of Jz and lower values of B and b.}     

One-dimensional Anderson model with dichotomic correlation in the presence of external electric field

A one-dimensional diagonal tight binding electronic system with dichotomic correlated disorder in the presence of external d.c field is investigated. It is found numerically that the conductance distribution obeys fairly well to log-normal distribution in weak disorder strength in localized regime, which indicates validity of single parameter scaling theory in this limit. Contrary to the universal cumulant relation C ₁ = 2C ₂ in the absence of d.c. field, we demonstrated numerically that C ₁ ≫ 2C ₂ in the presence of the field in localized regime. We interpret this result as suppression of the fluctuation effects by the external field. In addition, it is obtained that the quantity NF _c , here N is the system size and F _c is the crossover field, decreases as the as the system energy E increases. Moreover, we find numerically a simple linear relation between the average logarithm of the conductance 〈ln(g)〉 and the field strength as 〈ln(g)〉 = C(N, λ)F, here C(N, λ) is a constant for particular values of N and λ, which is the Poisson parameter of the dichotomic process.     

Information-theoretical complexity for the hydrogenic abstraction reaction

In this work, we have investigated the complexity of the hydrogenic abstraction reaction by means of information functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e. the I–D, D–L and I–J planes and the Fisher–Shannon and López–Mancini–Calbet (LMC) shape complexities. The analysis of the information-theoretical functionals of the one-particle density was computed in position (r) and momentum (p) space. The analysis revealed that all of the chemically significant regions can be identified from the information functionals and most of the information-theoretical planes, i.e. the reactant/product regions (R/P), the transition state (TS), including those that are not present in the energy profile such as the bond cleavage energy region (BCER), and the bond breaking/forming regions (B–B/F). The analysis of the complexities shows that, in position as well as in the joint space, the energy profile of the abstraction reaction bears the same information-theoretical features as the LMC and FS measures. We discuss why most of the chemical features of interest, namely the BCER and B–B/F, are lost in the energy profile and that they are only revealed when particular information-theoretical aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.     

Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt

The magnetic moments of the fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt were investigated by first-principles calculations based on density functional theory. The magnetic moments in fcc/fcc were larger than those of the bulk fcc, while the variations in the magnetic moment were complicated in hcp/hcp and fcc/hcp. The magnetovolume effect on the magnetic moment at the twin(-like) boundaries was investigated in terms of the local average atomic distance and the average deviation from equilibrium; however, the complicated variations in the magnetic moment could not be explained from the magnetovolume effect. Next, the narrowing (or broadening) of the partial density of states (PDOS) width of 3d orbitals, the number of occupied states for the spin-down channel, and the PDOS around the Fermi level were investigated. The entire variation in the magnetic moment at the twin(-like) boundaries could be understood in terms of these factors. Charge transfer occurred in hcp/hcp. In this case, the contributions of 4s and 4p electrons to the variation in the magnetic moment were relatively large.     

Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

Dispersion of quasi-particles in high Tc cuprates

The interplay between superconductivity (SC) and antiferromagnetism (AFM) is studied in strongly correlated systems of high T _c Cuprate superconductors. It is assumed that superconductivity arises due to BCS pairing mechanism in presence of AFM in Cu lattices of Cu-O planes. The total Hamiltonian of the system is mean field one and has been solved exactly by writing the equations of motion for the single particle Green’s functions. Equations for the appropriate single particle co-relation functions are derived and the order parameters corresponding to SC and AFM are determined. It is assumed that the Fermi energy ∈ _F = 0 and the renormalized localized f energy level coincide with the Fermi level. All the quantities in the final equation for h and Δ are made dimensionless by dividing by 2t, where t is the hopping integral. The temperature dependent values of staggered magnetic field (h) and SC gap (Δ) were determined by solving self-consistent equations for h and Δ. The quasiparticle energy bands are function of AFM gap (h), SC gap (Δ) and hybridization (V). Then the dispersion of quasi-particles are studied at different temperatures by considering temperature dependent values of h and Δ and varying other different model parameters.      

Slope parameter and scaling of differential cross-section of Λ-p scattering

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC ₁ +C ₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.     

Nonlinear optical effects for plasma diagnostics

Experimental investigations show that the 1/f noise intensityC and the contact resistanceR can be used to analyse contacts. The simply prepared contacts are fritted by discharging a capacitor, resulting in a multi-spot contact. A model relatesC andR to a number of contact spotsk with radiusa. More impulse-frittings at increasing energies decreaseC andR, thus enhancing the values ofk anda. From experimentalC vsR plots two regions are determined for GaAs: A fritting (a=constant) and A+B fritting (a∝k). Calculated values ofk are in good agreement with the number of peaks or pits formed by etching the semiconductor surface. From experimentalC vsW orR vsW curves, withW the cumulative impulse-fritting energy, the conclusion can be made thatka ³ is proportional toW.     

Large-scale flow structures in a planar offset attaching jet with a co-flowing wall jet

Conditional averaging techniques were used to examine the periodic motions that were observed in flows consisting of an offset planar jet and a co-flowing planar wall jet. The offset jet is one jet height (H_j) away from the wall and has a Reynolds number of approximately 40, 000, based on H_j and flow-rate averaged velocity U_o; for the co-flowing jets, different heights (i.e., 0.18H_j and 0.5H_j) and velocities (i.e., 0.56U_o and 0.36U_o) were considered. The flows had periodic motions with frequencies fH_j/U_o = 0.28 and 0.49 or fH_c/U_o = 0.23 and 0.25, where H_c is the distance between the jets. The periodic motions were present in both the inner shear layer of the offset jet above the re-circulation region and the outer shear layer of the wall jet below the re-circulation region. The motions from the inner shear layer of the offset jet persisted in the shear layer that formed downstream of the re-circulating region. There were periodic motions in the outer shear layer of the offset jet particularly in the flow with the smaller wall jet. The relative contribution of the motions to the total fluctuations increased as the flow evolved downstream reaching a maximum approximately 4H_c downstream of the flow exit. The relative contribution of the periodic motions to the turbulent fluctuations was similar in the two flows but the periodic motions had a much larger impact on the near-wall velocity and pressure fluctuations in the flow with the smaller wall jet due to the trajectory of the periodic structures, the distance of the periodic structures to the wall and the size of these structures.     

Systematic trends in the line strengths of E1 transitions in the oxygen isoelectronic sequence

Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ ² S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s²2s²2p^{4 1}S.     

Enhancement in age hardenability of sintered Ti–5Fe alloy by Zr addition processed by pulsed electric current sintering

The age-hardenable Ti–5Fe–5Zr (wt. %, 5Zr) alloy has been consolidated by pulsed electric current sintering, following a β solution treatment, and the results are compared with a Ti–5Fe (0Zr) alloy. The precipitation sequence measured at 640°C ageing is β?+?athermal ω?→?β?+?isothermal ω?→?β?+?α. At the peak hardness isothermal ω phase forms at 20?s of ageing. The Zr addition retards the precipitation kinetics of the α phase; as a result, the α phase nucleates at latest at 300?s ageing in the overaged state. Fe is partitioned into β, while it is depleted from the α phases. There is Zr enrichment near the α/β interface when the α phase precipitates due to a solute drag effect; the growth rate of the α phase in the 5Zr alloy is significantly reduced compared with that in the 0Zr alloy.     

Solvable models of temporally correlated random walk on a lattice

We seek the conditional probability functionP(m,t) for the position of a particle executing a random walk on a lattice, governed by the distributionW(n, t) specifying the probability ofn jumps or steps occurring in timet. Uncorrelated diffusion occurs whenW is a Poisson distribution. The solutions corresponding to two different families of distributionsW are found and discussed. The Poissonian is a limiting case in each of these families. This permits a quantitative investigation of the effects, on the diffusion process, of varying degrees of temporal correlation in the step sequences. In the first part, the step sequences are regarded as realizations of an ongoing renewal process with a probability densityψ(t) for the time interval between successive jumps.W is constructed in terms ofψ using the continuous-time random walk approach. The theory is then specialized to the case whenψ belongs to the class of special Erlangian density functions. In the second part,W is taken to belong to the family of negative binomial distributions, ranging from the geometric (most correlated) to the Poissonian (uncorrelated). Various aspects such as the continuum limit, the master equation forP, the asymptotic behaviour ofP, etc., are discussed.     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

New explicit nonperiodic solutions of the homogeneous wave equation

We exhibit a newansatz for the solution of the homogeneous three-dimensional time-dependent wave equation in spherical coordinates of the form Φ(r,t)=Y(θ, φ)(I(r)+G(g)), whereg ≡ct/r. FunctionG(g) has explicit solution in terms of three independent nonperiodic functionss _ℓ,t _ℓ,u _ℓ (s _ℓ andt _ℓ are related to the associated Legendre functions of the first and second kinds).G(g) is nonperiodic and may be cast as a superposition of incoming and outgoing waves. To obtainG(g), we solved a nonhomogeneous associated Legendre equation (this solution, to our knowledge, is also new).G(g) may prove useful in many microscopic and macroscopic problems, representable by homogeneous wave equations.