Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period e{\epsilon} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.     

Effect of K doping on the physical properties of La0.65Ca0.35−xKxMnO3 (0?x?0.2) perovskite manganites

The effects of K doping in the A-site on the structural, magnetic and magnetocaloric properties in La_0.65Ca_0.35−xK_xMnO₃ (0?x?0.2) powder samples have been investigated. Our samples have been synthesized using the solid-state reaction method at high temperature. The parent compound La_0.65Ca_0.35MnO₃ is an orthorhombic (Pbnm space group) ferromagnet with a Curie temperature T_C of 248 K. X-ray diffraction analysis using the Rietveld refinement show that all our synthesized samples are single phase and crystallize in the orthorhombic structure with Pbnm space group for x?0.1 and in the rhombohedral system with R3¯c space group for x=0.2 while La_0.65Ca_0.2K_0.15MnO₃ sample exhibits both phases with different proportions. Magnetization measurements versus temperature in a magnetic applied field of 50 mT indicate that all our investigated samples display a paramagnetic-ferromagnetic transition with decreasing temperature. Potassium doping leads to an enhancement in the strength of the ferromagnetic double-exchange interaction between Mn ions, and makes the system ferromagnetic at room temperature. Arrott plots show that all our samples exhibit a second-order magnetic-phase transition. The value of the critical exponent, associated with the spontaneous magnetization, decreases from 0.37 for x=0.05 to 0.3 for x=0.2. A large magnetocaloric effect (MCE) has been observed in all samples, the value of the maximum entropy change, |ΔS_m|_max, increases from 1.8 J/kg K for x=0.05 to 3.18 J/kg K for x=0.2 under a magnetic field change of 2 T. For x=0.15, the temperature dependence of |ΔS_m| presents two maxima which may arise from structural inhomogeneity.     

Asymmetric Cycloaddition: An Efficient Synthesis of Enantiopure Isoxazolines Substituted with Carbohydrate Analogues

A simple and convenient method for the synthesis of heterocycles substituted with carbohydrate analogs is described. The chiral optically pure five‐membered glycoconjugates containing the isoxazoline unit were obtained by an aromatic nitrile oxides cycloaddition with 1‐phenyl‐1,2‐dihydro‐pyridazine‐3,6‐dionyl N‐glycoside derivatives.     

Polaronic and charge ordering effects in Pr 0.5 Sr 0.5 Mn 1− x Fe x O 3

In this work we report the results of X-ray diffraction and Mössbauer spectroscopy for the systems Pr_0.5Sr_0.5Mn_1???x Fe _x O₃ (with x?=?0.05, 0.10, 0.15, 0.20, 0.25, 0.30). XRD patterns indicated that all samples were single phase with slightly distorted orthorhombic symmetry. Room temperature Mössbauer spectra are all quadrupole split, indicating paramagnetic relaxation of the Fe moment for all values of Fe concentrations. The spectra are fitted with two doublet components associated with Fe^3?+? ions in octahedral sites with different distortions. Mössbauer spectra recorded at liquid nitrogen temperature for this system also indicate paramagnetic relaxation of the Fe moments down to liquid nitrogen temperature (LNT). In these spectra a third quadrupole component with quadrupole splitting close to zero develops. This component is associated with the delocalization of the charge carriers and the consequent disappearance of lattice distortions produced by the polaronic effect at room temperature. The component with the high quadrupole splitting (0.81 to 1.07 mm/s) results from Jahn–Teller distortion as a consequence of charge ordering transition at low temperature.     

Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicity

We study the limiting behavior of a nonlinear Schrödinger equation describing a 3-dimensional gas that is strongly confined along the vertical, z direction. The confinement induces fast oscillations in time, that need to be averaged out. Since the Hamiltonian in the z direction is merely assumed confining, without any further specification, the associated spectrum is discrete but arbitrary, and the fast oscillations induced by the nonlinear equation entail countably many frequencies that are arbitrarily distributed. For that reason, averaging cannot rely on small denominator estimates or like.To overcome these difficulties, we prove that the fast oscillations are almost-periodic in time, with values in a Sobolev-like space that we completely identify. We then exploit the existence of long-time averages for almost-periodic functions to perform the necessary averaging procedure in our nonlinear problem.     

A mathematical model for the transient evolution of a resonant tunneling diodeModélisation d'une diode à effet tunnel résonant en régime transitoire

A mathematical model of quantum transient transport is derived and analyzed. The model describes the evolution of electrons injected into the “device” by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properies” of the boundary conditions and from the repulsive character of the electrostatic interaction. To cite this article: N. Ben Abdallah, O. Pinaud, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 283–288.     

Chemo- and Regioselective 1,3-Dipolar Cycloaddition of 2-Diazopropane over 1,4-Benzoquinone: Synthesis of New Pyrazoloquinones

Abstract

1,3-Dipolar cycloaddition reaction of 2-diazopropane 1 with 1,4-benzoquinone 2 carried out at ?20 °C led to a minor mono-cycloadduct 4 and mixture of bis-cycloadducts 6 and 7. The same addition realized with 3H-pyrazole 7 at ?60 °C for 2 h yields a mixture of compounds 8 and 9 and results in O-alkylation. The reaction of 3H-pyrazoles 4 and 7 with dimethylsulfoxide and oxalyl chloride under Swern conditions led to pyrazolenines 11 and 12.     

Effect of trivalent rare earth doping on magnetic and magnetocaloric properties of Pr<Subscript>0.5</Subscript>(Ce,Eu,Y)<Subscript>0.1</Subscript>Sr<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> manganites

Experimental studies of the structural, magnetic and magnetocaloric properties of the three compounds Pr_0.5X_0.1Sr_0.4MnO₃ (X = Ce, Eu and Y) are reported. Our samples were synthesized using the Pechini sol–gel method. X-ray powder diffraction at room temperature indicates that our materials crystallize in the orthorhombic structure with Pbnm space group. The compounds undergo a second-order magnetic transition from paramagnetic to ferromagnetic state around their own Curie temperatures T _C ~ 310, 270 and 230 K for X = Ce, Eu and Y, respectively. A considerable magnetocaloric effect (MCE) is observed around room temperature. The maximum values of magnetic entropy change ?S _max are 3.54, 3.81 and 2.99 J/kgK for the samples with X = Ce, Eu and Y, respectively, when a magnetic field of 5 T was applied. The relative cooling power (RCP) values for the corresponding materials are 246.60, 261.66 and 298 J/kg. It is shown that for Pr_0.5X_0.1Sr_0.4MnO₃ the exponent n and the magnetic entropy change follow a master curve behavior. With the universal scaling curve, the experimental ?S at several temperatures and fields can be extrapolated.