Three impurity cluster in a diatomic linear chain

The modes of vibration of a three impurity cluster in a diatomic linear chain is studied. The configuration of the three impurity atoms is such that two of these go into next nearest neighbour sites in one of the sub-lattices whereas the third occupies the central in between site in the other sub-lattice. New local, gap and inband modes are seen to exist, besides the ones corresponding to the impurity pairs. A new feature which appears is that the frequencies of some of the pair modes remain totally unaffected in the presence of the third impurity atom.     

Two-phonon bound states in imperfect crystals

The question of the occurrence of two-phonon bound states in imperfect crystals is investigated. It is shown that the anharmonicity mediated two-phonon bound state which is present in perfect crystals gets modified due to the presence of impurities. Moreover, the possibility of the occurrence of a purely impurity mediated two-phonon bound state is demonstrated. The bound state frequencies are calculated using the simple Einstein oscillator model for the host phonons. The two-phonon density of states for the imperfect crystal thus obtained has peaks at the combination and difference frequencies of two host phonons besides the peaks at the bound state frequencies. For a perfect crystal the theory predicts a single peak at the two-phonon bound state frequency in conformity with experimental observations and other theoretical calculations. Experimental data on the two-phonon infrared absorption and Raman scattering from mixed crystals of GA_1−c Al _c P and Ge_1−c Si _c are analysed to provide evidence in support of impurity-mediated two-phonon bound states. The relevance of the zero frequency (difference spectrum) peak to the central peak observed in structural phase transitions, is conjectured; This work is a part of the thesis to be submitted by one of the authors (SS) in partial fulfilment of the degree of Doctor of Philosophy to Utkal University, Bhubaneswar, India.     

Solution to fuzzy system of linear equations with crisp coefficients

This paper presents a new and simple method to solve fuzzy real system of linear equations by solving two n × n crisp systems of linear equations. In an original system, the coefficient matrix is considered as real crisp, whereas an unknown variable vector and right hand side vector are considered as fuzzy. The general system is initially solved by adding and subtracting the left and right bounds of the vectors respectively. Then obtained solutions are used to get a final solution of the original system. The proposed method is used to solve five example problems. The results obtained are also compared with the known solutions and found to be in good agreement with them.     

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions

The classical φ⁶-field theory in (1+1) dimensions, is considered as a model for the first order structural phase transitions. The equation of motion is solved exactly; and the presence of domain wall (kink) solutions at and below the transition point, in addition to the usual phonon-like oscillatory solutions, is demonstrated. The domain wall solutions are shown to be stable, and their mass and energies are calculated. Above the transition point there exists exotic unstable kink-like solutions which takes the particle from one hill top to the other of the potential. The partition function of the system is calculated exactly using the functional integral method together with the transfer matrix techniques which necessitates the determination of the eigenvalues of a Schrödinger-like equation. Thus the exact free energy is evaluated which in the low temperature limit has a phonon part and a contribution coming from the domain wall excitations. It was shown that this domain wall free energy differs from that calculated by the use of the domain wall phenomenology proposed by Krumhansl and Schrieffer. The exact solutions of the Schrödinger-like equation are also used to evaluate the displacement-displacement, intensity-intensity correlation functions and the probability distribution function. These results are compared with those obtained from the phenomenology as well as the φ⁴-field theory. A qualitative picture of the central peak observed in structural phase transitions is proposed.     

Evidence for B-->phiphiK

We report evidence for the decay mode B-->phiphiK based on an analysis of 78 fb(-1) of data collected with the Belle detector at KEKB. This is the first example of a b-->sssss transition. The branching fraction for this decay is measured to be B(B+/--->phiphiK+/-)=(2.6(+1.1)(-0.9)+/-0.3)x10(-6) for a phiphi invariant mass below 2.85 GeV/c(2). Results for other related charmonium decay modes are also reported.     

Studies of the decay B+/- -->D(CP)K+/-

We report studies of the Cabibbo-suppressed decay B+/--->D(CP)K+/-, where D(CP) denotes CP eigenstates of the D0-D0; system. The analysis is based on a 29.1 fb(-1) sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e(+)e(-) storage ring. We measure ratios of branching fractions, relative to Cabibbo-favored B+/--->D(CP)pi(+/-), of B(B--->D1K-)/B(B--->D1pi(-))=0.125+/-0.036+/-0.010 and B(B--->D2K-)/B(B--->D2pi(-))=0.119+/-0.028+/-0.006; the index 1 (2) denotes the CP=+1 (-1) eigenstate. We also extract the partial rate asymmetries for B+/--->D(CP)K+/-, finding A(1)=0.29+/-0.26+/-0.05 and A(2)=-0.22+/-0.24+/-0.04.     

Measurement of the CP violation parameter sin2 phi(1) in B(0)(d) meson decays

We present a measurement of the standard model CP violation parameter sin2 phi(1) (also known as sin2beta) based on a 10.5 fb(-1) data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e(+)e(-) collider. One neutral B meson is reconstructed in the J/psiK(S), psi(2S)K(S), chi(c1)K(S), eta(c)K(S), J/psiK(L), or J/psipi(0) CP-eigenstate decay channel and the flavor of the accompanying B meson is identified from its charged particle decay products. From the asymmetry in the distribution of the time interval between the two B-meson decay points, we determine sin2 phi(1) = 0.58(+0.32)(-0.34)(stat)+0.09-0.10(syst).     

Theory of two-phonon modes in layered charge-density-wave systems

A theoretical model with electron-phonon and anharmonic interactions is proposed to explain the two-phonon mode observed in the Raman spectra of layered transition metal dichalcogenides, which exhibit charge density wave (cdw) phase transition. The phonon self-energy, which involves the electron response function and the two-phonon Green’s function, is calculated using the double-time Green’s function formalism. It is shown that in these low-dimensional systems there exists an anharmonicity-mediated two-phonon mode in the phonon spectral function both in the normal and in thecdw phases. In the normal phase since the phonon Raman scattering proceeds through a single optic phonon the calculations are carried out for zero wave vector and hence the contribution of the electron response function to the self-energy vanishes. On the other hand explicit evaluation of the two-phonon Green’s function shows that the frequency of the two-phonon mode is twice that of the Kohn anomaly phonon and decreases with decreasing temperature. The strength of two-phonon peak is found to be comparable to that of the original optic phonon. In thecdw phase the phonon which enters into the Raman scattering is taken to be the one with thecdw wave vectorQ, which when zone-folded becomes equivalent to zero wave vector. The evaluation of the electron response function in this phase generates a phonon corresponding to thecdw-amplitude mode. The two-phonon Green’s function is assumed to be of similar form as in the normal phase. The spectral function evaluated at zero temperature shows a weak two-phonon peak besides the prominentcdw-amplitude mode. Numerical results are presented for the system 2H-NbSe₂ and are found to be in qualitative agreement with the experimental data.     

Lattice dynamics of impurity clusters. Application to pairs

A general solution is obtained for the lattice dynamics of a cluster ofn-impurity atoms using the double-time Green’s function formalism. The cluster is characterized byn-mass defect andm-force constant change parameters. It is shown that this general solution for the Green’s function for then-impurity cluster can also be expressed in terms of the Green’s function for the (n−1)-impurity cluster. As an application, the cluster impurity modes for a pair are calculated using the Debye model for the host lattice dynamics. The splitting of the high frequency local modes and nearly zero frequency resonant modes due to pairs show an oscillatory behaviour on varying the distance of separation between the two impurity atoms. These oscillations are most prominent for two similar impurities and get damped for two dissimilar impurities or if one of the impurities produces a force constant change. The predictions of the calculation provide qualitative explanation of the data obtained from the infrared measurements of the resonant modes in mixed crystal system of KBr_1−c Cl _c : Li⁺ and KBr_1−c I _c : Li⁺.     

An organically templated Co(II) sulfate with the kagome lattice

An amine-templated cobalt(II) sulfate with the kagome lattice, prepared for the first time, exhibits magnetic properties comparable to those of the analogous Fe(III) compounds.