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.     

Translationally invariant kink solutions of discrete ϕ<Superscript>4</Superscript> models

The properties of translationally invariant kinks in two discrete ϕ⁴ models are compared with those of the kinks in a classical discrete model. The translationally invariant kink solutions can be found randomly with respect to the lattice sites, i.e., their Peierls–Nabarro potential is exactly equal to zero. It is shown that these solutions have a Goldstone mode, that is, they can move along the lattice at vanishingly small velocities. Thus, the translationally invariant kink is not trapped by the lattice and can be accelerated by an arbitrary small external field and, having an increased mobility, can transfer a range of physical quantities: matter, energy, momentum, etc.     

Observation of penning ionization in Zr-Ne discharge by optogalvanic effect

The pulsed optogalvanic (OG) effect is used to observe Penning ionization in a Zr-Ne hollow-cathode discharge, which was axially irradiated by a pulsed dye laser pumped by copper vapor laser. The effect of discharge current on the temporal evolution of the OG signal is studied at 588.2, 594.5, 597.6 and 614.3 nm. The double humped temporal profile of the OG signals, corresponding to transitions of neon, and closeness of energy levels between that level of neon (Ne) and excited levels of zirconium (Zr) ions confirmed that Penning type of ionizing energy transfer collisions were taking place in the Zr-Ne discharge at lower discharge currents (≤5 mA). The disappearance of the double humped feature in the temporal profile of the OG signals indicated that the Penning contribution became negligible at higher discharge currents (≥10 mA).     

Low frequency dielectric spectroscopy of two room temperature chiral liquid crystal mixtures

Dielectric spectroscopy of two room temperature chiral liquid crystal mixtures (W-96 and W-97) have been carried out in the frequency range of 100?mHz–10?MHz. Low frequency dielectric relaxation modes corresponding to collective behavior of molecules (Goldstone- and soft-modes) in the SmC* phase have been found to be masked by the ionic conductance. Two slow modes of dielectric relaxation due to the ionic conductance have been detected (below 15?Hz) in planar-aligned samples. It has been observed that the effect of ionic conductance decreases with the number of thermal annealing cycles on the materials. With large number of thermal annealing cycles it has been possible to wipe out the effects of ionic conductance and then to detect other weak modes of dielectric relaxation which are otherwise masked.     

Landau theory of ferroelectric transition in long cylindrical nanoparticles

Using a phenomenological Landau theory, the size dependence on ferroelectric transition for free-standing long cylindrical nanoparticles is discussed. We derive the size dependence of the transition temperature, polarization profile as well as the static susceptibility. The transition temperature vanishes below a critical size where the static susceptibility shows divergence obeying Curie-Weiss law. In order to make this result compared with experiments, the average polarization and the susceptibility is computed with a Gaussian particle size distribution. The average polarization in such a case shows smearing with respect to the particle size whereas the divergence in the susceptibilty gets rounded. This might correspond to a size dependent soft mode which can be observed in Raman measurement.     

Synergistically advancing Li storage property of hydrothermally grown 1D pristine MnO2 over a mesh-like interconnected framework of 2D graphene oxide

Journal of Solid State Electrochemistry - Here, we present a unique morphology comprising a blend of ultrafine 1D MnO2 and graphene oxide as an efficient anode material to overcome the issue of...     

Reactivity of M(en)Cl2 (M = Pd/Pt,en = 1,2-diaminoethane) with N,N′-bis(salicylidene)-p-phenylenediamine: Binding with hexafluorobenzene

Schiff base N,N′-bis(salicylidene)-p-phenylenediamine (LH₂) complexed with Pt(en)Cl₂ and Pd(en)Cl₂ provided [Pt(en)L]₂ · 4PF₆ (1) and Pd(Salen) (2) (Salen = N,N′-bis(salicylidene)-ethylenediamine), respectively, which were characterized by their elemental analysis, spectroscopic data and X-ray data. A solid complex obtained by the reaction of hexafluorobenzene (hfb) with the representative complex 1 has been isolated and characterized as 3 (1 · hfb) using UV–Vis, NMR (¹H, ¹³C and ¹⁹F) data. A solid complex of hfb with a reported Zn-cyclophane 4 has also been prepared and characterized 5 (4 · hfb) for comparison with complex 3. The association of hfb with 1 and 4 has also been monitored using UV–Vis and luminescence data.