International Journal of Modern Physics B

In the present study we report on the formation mechanism of some binary Al-TM and ternary Al-Cu-TM (TM = transition metal) quasicrystals. We have found that the formation mechanism of quasicrystalline phases in the binary Al-TM system takes place at extremely high solidification rates, is linked to the location of the transition metal in the periodic table, depends upon the atomic radius ratio of the constituents, is composition sensitive, and as a result is strongly affected by the effective atomic radius ratio (a_eff). Applying empirical criteria on the formation of ternary Al-Cu-TM quasicrystals we were able to calculate the composition range at which the formation tendency and stability of quasicrystalline phases is enhanced. The method presented can be viewed as an empirical criterion to find new and high quality quasicrystalline materials and to optimize the quasicrystalline material composition. Furthermore, it was observed that the stabilization mechanism of the quasicrystalline Al-Cu-(Fe, Co, Ru, Rh, Os, Ir) phases takes place when the atomic ratio (TM+Cu)/Al ranges from 0.46 to 0.69 and for a_eff values between 4.10 and 7.30. At the same valence electron concentration, metastable icosahedral Al-Cu-(Cr, Mn) phases are formed at relatively smaller atomic ratios (TM+Cu)/Al and having higher a_eff values in comparison to those of the stable D- and I-phases.

We use the two-dimensional Fermion-Boson mapping to perform a field theory analysis of the effective Lagrangian model for incommensurate charge-density waves (ICDW) in one-dimensional systems. We consider an approach in which both the phase of the complex phonon field and the electron field are dynamical degrees of freedom contributing to the quantum dynamics and symmetry-related features of the ICDW phenomenon. We obtain the bosonized and fermionized versions of the effective electron–phonon Lagrangian. The phase of the phonon field and the phase of the bosonized chiral density of the electron field condense as a soliton order parameter, carrying neither the charge nor the chirality of the electron–phonon system, leading to a periodic sine-Gordon potential. The phonon field is fermionized in terms of a chiral fermionic condensate and the effective model is mapped into the chiral Gross–Neveu (GN) model with two Fermi field species. The linked electron–phonon symmetry of the ICDW system is mapped into the chiral symmetry of the GN model. Within the functional integral formulation, we obtain for the vacuum expectation value of the phonon field < ϕ > = 0 and < ϕ ϕ* > ≠ 0, due to the charge selection rule associated with the chiral electron–phonon symmetry. We show that the two-point correlation function of the phonon field satisfies the cluster decomposition property, as required by the chiral symmetry of the underlying GN model. The quantum description of the ICDW corresponds to charge transport through the lattice, due to the propagation of a "Goldstone mode" carrying the effective charge of the electron–phonon system, is accomplished by an electron–lattice energy redistribution. This accounts for a dynamical Peierls's energy gap generation.

A multi-level evolution model where forced extinctions occur throughout the system based on a species fitness value (or survivability) is developed that is essentially the fusion of the evolution model of Bak and Sneppen and the food-web model of Amaral and Meyer. This model is found to describe the fossil record and behave as a self-organized critical system with a power law exponent of approximately 2, but is also found to be remarkably similar to a model that causes the forced extinctions randomly throughout the system. To explain this result we show that fitness is nearly randomly distributed with a slight peak in forced extinction (due to fitness) in the middle levels. These findings lend strong support to the hypothesis that coextinction effects (propagated through a food-web) provide a robust explanation of the fossil record, independent of the mechanism for species competition.

We used dynamical invariant operator method to find the quantum mechanical solution of a harmonic plus inverse harmonic oscillator with time-dependent coefficients. The eigenvalue of invariant operator is obtained and is constant with time. We constructed lowering and raising operators from the invariant operator. The solution of Schrödinger equation is obtained using operator method. We have also used ladder operators to obtain various expectation values of the time-dependent system. The results in this manuscript are not only more general than the existing results in the literatures but also well match with others.

We study the longitudinal dynamical spin susceptibility within the framework of Heisenberg model in the ferromagnetic phase, where no external field exists. On the basis of memory function formalism within the framework of the irreducible Green's functions we obtained the self-consistent equations for in mode coupling approximation. The expression for the longitudinal spin susceptibility is valid in the whole range of system frequencies. Its validity in the range of low and high frequencies was discussed in particular for the magnetic systems in ferromagnetic phase.

Impedance spectroscopy studies of calcium doped (Ca=0.01, 0.05, 0.1) sodium bismuth titanate (NBT), that is, (Na_1/2Bi_1/2)_1-xCa_xTiO₃ (NBCT) solid solution are studied as a function of temperature (RT — 575°C) and frequency (100 Hz–1 MHz). The electrical properties and equivalent circuit parameters of Ca doped NBT, and it's bulk and grain boundary effects are studied with impedance spectroscopy as a non-destructive testing tool.

We consider a single Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We investigate the quantum dynamics of the Cooper-pair box and show that the collapse and revival phenomena can exist in this system, which is sensitive to the detuning between the Josephson energy E_J and cavity field frequency ω.

Two analytical techniques for the determination (within the limits of validity of the free electron model) of the absolute atom concentration (AAC) are reported in details. One of these may be useful for the determination of a AAC for chemical elements (e.g. hydrogen) which are not easy to detect. EELS is used.

A new variational ansatz for the coherent phonons with correlated displacement and squeezing, including interaction with electrons are used to study the properties of (i) the nonadiabatic phonon fluctuation on the ground state, (ii) the uncertainty principle, (iii) the phonon-staggered ordering, and (iiv) the charge-density wave order, of the systems due to fluctuations of the electron density in a coupled electron–phonon systems. The results obtained show that the correlation effect can lower the energy of the ground state of the systems, enhance the stabilization of the polaron and suppress the quantum increase of the classical polaron narrowing of electron band. Moreover, it add to the effects of nonadiabaticity on the minimum quantum uncertainty for the phonon coordinate by a strong coupling with the electron density for a large squeezing as compared with the adiabatic case and the uncorrelated case. Therefore, the new ansatz which can represent the correlation effects of displacement and squeezing is especially relevant for system with sufficiently large squeezing and strong coupling.