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The problem of an exciton trapped in a Gaussian quantum dot (QD) of GaAs is studied in both two and three dimensions in the presence of an external magnetic field using the Ritz variational method, the 1/N expansion method and the shifted 1/N expansion method. The ground state energy and the binding energy of the exciton are obtained as a function of the quantum dot size, confinement strength and the magnetic field and compared with those available in the literature. While the variational method gives the upper bound to the ground state energy, the 1/N expansion method gives the lower bound. The results obtained from the shifted 1/N expansion method are shown to match very well with those obtained from the exact diagonalization technique. The variation of the exciton size and the oscillator strength of the exciton are also studied as a function of the size of the quantum dot. The excited states of the exciton are computed using the shifted 1/N expansion method and it is suggested that a given number of stable excitonic bound states can be realized in a quantum dot by tuning the quantum dot parameters. This can open up the possibility of having quantum dot lasers using excitonic states.

The quantum transport properties of a single molecular transistor are studied in the presence of an external magnetic field using the Keldysh Green function technique. The Anderson-Holstein-Caldeira-Leggett model is used to describe the single molecular transistor that consists of a molecular quantum dot (QD) coupled to two metallic leads and placed on a substrate that acts as a heat bath. The local electron-phonon (el-ph) interaction in the QD is decoupled by the Lang-Firsov (LF) transformation and the effective Hamiltonian is used to study the effects of an external magnetic field on the tunneling current and spin polarization of a SMT at zero temperature.The quantum transport properties of a single molecular transistor are studied in the presence of an external magnetic field using the Keldysh Green function technique. The Anderson-Holstein-Caldeira-Leggett model is used to describe the single molecular transistor that consists of a molecular quantum dot (QD) coupled to two metallic leads and placed on a substrate that acts as a heat bath. The local electron-phonon (el-ph) interaction in the QD is decoupled by the Lang-Firsov (LF) transformation and the effective Hamiltonian is used to study the effects of an external magnetic field on the tunneling current and spin polarization of a SMT at zero temperature.

A single-level Anderson–Holstein model is studied using the Lang–Firsov transformation followed by a zero-phonon averaging and a Green function method within the framework of a mean-field approximation. The ground state energy of the system, the binding energy between the impurity and conduction electrons, and the impurity–electron spectral function are calculated. The effect of the electron–phonon interaction on the local moment as well as on the specific heat of the impurity electron is explored in the anti-adiabatic regime.

The effect of electron–phonon interaction on the spectral function of a magnetic impurity in a non-magnetic host metal is studied within the framework of the Anderson–Holstein model using a spectral density method. The impurity contribution to the specific heat of the host metal is also calculated.

Elbasvir a NS5A inhibitor is used in combination of Grazoprevir (NS3/4A protease inhibitor) for the treatment of chronic Hepatitis C, an infectious liver disease caused by infection with Hepatitis C Virus (HCV) under the trade name Zepatiar®. A stability indicating reverse phase HPLC method was developed and validated for the determination of Elbasvir and Grazoprevir in tablet dosage form. A waters Alliance HPLC with Zorbax eclipse XDB C18 (250 x 4.6 mm) 3.5μ columnwas used for chromatographic separation. A mobile phase consisting of potassium dihydrogen phosphate buffer pH adjusted to 4.0: acetonitrile (40: 60v/v) with a flow rate of 1.0 mL/min was used, the UV detection was carried out at 260 nm. The established method was linear, accurate and precise over the range of 12.5 to 75 μg/mL with a regression equation of Y=20782X+2849.4 and correlation coefficient of 0.9995for elbasvir and linear over the range of 25–150 μg/mL with a regression equation of Y=14897X+20611 and correlation coefficient of 0.9992for Grazoprevir. The validated method demonstrated high sensitivity, accuracy, precision, selectivity and robustness. The method demonstrated high selectivity in presence of degradants produced during the stress conditions when Elbasvir and Grazoprevir were subjected to acid, alkali, oxidation, thermal and photolytic degradation.

The Anderson-Holstein model with Caldeira-Leggett coupling with environment is considered to describe the damping effect in a single molecular transistor (SMT) which comprises a molecular quantum dot (with electron-phonon interaction) mounted on a substrate (environment) and coupled to metallic electrodes. The electron-phonon interaction is first eliminated using the Lang-Firsov transformation and the spectral density function, charge current and differential conductance are then calculated using the non-equilibrium Keldysh Green function technique. The effects of damping rate and electron-electron and electron-phonon interactions on the transport properties of SMT are studied at zero temperature.

The single-impurity Anderson-Holstein model is investigated in the presence of a magnetic field by an improved variational method. The phonon degrees of freedom are first eliminated by a modified Lang-Firsov transformation followed by a zero-phonon averaging. The resulting Hamiltonian is then treated by a cluster variational method to study the effects of the electron-phonon interaction and the magnetic field on the ground state energy, local magnetic moment and the binding energy between the magnetic impurity and the conduction electrons.

A single-level Anderson-Holstein model is investigated using the Lang-Firsov transformation followed by a zero-phonon averaging and the Kikuchi-Morita Cluster variation method as adopted by Bose and Tanaka in the case of Anderson model. The ground state energy of the system at zero temperature and the binding energy between the magnetic impurity and the conduction electrons are calculated for the symmetric case ed = −(U/2). Subsequently, the effect of the electron-phonon interaction on the ground state energy and the binding energy is investigated.