Study of magnetoresistance and conductance of bicrystal grain boundary in La0.67Ba0.33MnO3 thin film

La_0.67Ba_0.33MnO₃ (LBMO) thin film is deposited on a 36.7°C SrTiO₃ bicrystal substrate using laser ablation technique. A microbridge is created across bicrystal grain boundary and its characteristics are compared with a microbridge on the LBMO film having no grain boundary. Presence of grain boundary exhibits substantial magnetoresistance ratio (MRR) in the low field and low temperature region. Bicrystal grain boundary contribution in MRR disappears at temperature T>175 K. At low temperature, I-V characteristic of the microbridge across bicrystal grain boundary is nonlinear. Analysis of temperature dependence of dynamic conductance-voltage characteristics of the bicrystal grain boundary indicates that at low temperatures (T<175 K) carrier transport across the grain boundary in LBMO film is dominated by inelastic tunneling via pairs of manganese atoms and tunneling through disordered oxides. At higher temperatures (T>175 K), magnetic scattering process is dominating. Decrease of bicrystal grain boundary contribution in magnetoresistance with the increase in temperature is due to enhanced spin-flip scattering process.     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

Mod pq Galois representations and Serre's conjecture

We consider linear representations of the Galois groups of number fields in two different characteristics and examine conditions under which they arise simultaneously from a motive.     

Multiplicities of modp Galois representations

We study the multiplicity with which 2-dimensional modp Galois representations occur in Jacobians of modular curves.     

QCD correction to the leptonic decay rate ofD-wave vector mesons

We show that the first order QCD correction to the leptonic decay rate of heavy quark-antiquark³ D ₁ bound state is identical to that for a³ S ₁ state. Some phenomenological implications of this suppression are also discussed.     

A comparison of different sudden approximations for molecular scattering

Total differential cross sections for collision between linear molecules and atoms are formulated and calculated in the framework of several approximations in the sudden limit in order to establish a practical method for a comparison with measured molecular beam data. The two extreme methods, the infinite order sudden and the first order linear trajectory approximation give results which differ by more than a factor of two in the anisotropy parameter. The origin of this difference lies mainly in the use of the linear trajectory. The infinite or first order treatment and the fixed or variable angle between the molecular axis and the atom during the collisions which are valid for the approximation, respectively, are only of minor influence on the result.     

Supersymmetry and solvable periodic potentials

We use the formalism of supersymmetric quantum mechanics to enlarge considerably the limited class of analytically solvable one-dimensional periodic potentials. In particular, we derive and discuss the energy-band structure of the Lamé potentials pm sn² (x, m) and associated Lamé potentials pm sn² (x, m) + qm cn²(x, m)/dn² (x, m), both of which involve Jacobi elliptic functions with modulus parameter m. We find several new analytic expressions for band-edge energies and wave functions. The supersymmetric partners of Lamé and associated Lamé potentials constitute even more new solvable potentials with exactly the same energy-band structure.     

Truncated harmonic oscillator and parasupersymmetric quantum mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary orderp can also be rewritten in terms ofp supercharges (i.e. all of which obeyQ _i ² =0). However, the Hamiltonian cannot be expressed in a simple form in terms of thep supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, thep supercharges, thep conformal supercharges along with HamiltonianH, conformal generatorK and dilatation generatorD form a closed algebra.     

CS(lav) and computational study of degeneracy averaged differerential cross sections and Δm-integral cross sections: Hez.sbndCO,HDz.sbnd

CC and l-average CS calculations of degeneracy averaged differential cross sections and Δm-integral cross sections have been performed for Hez.sbndCO at E = 60 cm^?1 and E = 80 cm^?1, for HDz.sbndNe at E = 254 cm^?1, and for Hez.sbndH₂ at E = 1520 cm^?1. The l_avz.sbndCS degeneracy averaged differential cross sections are generally in good agreement with the CC cross sections. The previously observed shifts in the diffraction oscillations for odd rotationally inelastic transitions for Hez.sbndCO and HDz.sbndNe do not occur due to proper phase choice and l? = l_av choice rather than l? = 1 or l′. The l_avz.sbndCS approximation gives reliable results for most Δm-integral cross sections except for those σ_cs(jm, jm′) cross sections for which the CC cross sections σ(jm;jm′) and σ(jm′;jm) differ by a large amount.