Nonlinear localized modes in PT-symmetric optical media with competing gain and loss

The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.Comment: Final versio

Analysis of pion nucleon scattering at high energies

A phenomenological analysis of Pion Nucleon scattering data at high and intermediate energies and at all angles has been undertaken. At high energies say above 5 GeV/c the differential cross sections are strongly peaked in the forward and backward directions and these peaks can be adequately explained by a small number of leading Regge poles in t channel (for the forward peak) and u channel (for the backward peak). In this work new Regge fits are performed to all available recent high energy data, to obtain the Regge parameters. Below 5 GeV/c down up to 2 GeV/c the forward and backward peaks are still very conspicuous and can still be explained by the Regge poles used in the high energy fits. So it is thought to be convenient to define an amplitude Fp(s,t,u) which is the difference between the total and the Regge amplitudes. A parametric form of this amplitude (viz, Fg) was taken to fit all data between 2 to 5 GeV/c simultaneously, while the parameters of the Regge Amplitudes are held fixed to their values obtained from high energy fits. First all Π-p scattering data were fitted to get I = 3/2 amplitude then Π- p and charge exchange data were fitted to obtain I = 1/2 amplitudes. Two different ways of parameterising Fg (s,t,u) have been attempted. The first was based on the direct channel Regge pole model with Khuri modification, and the second was of a simpler and less sophisticated phenomenological form, the amplitudes being expressed as a power series in Cos 0 ( being scattering angle) with energy dependent coefficients', the second method was found particularly successful in the present work. Partial Wave projections of both T = 1/2 and T = 3/2 amplitudes were made and the phase shifts were obtained for both the isospin amplitudes. Possibilities of the existence of resonances in the energy region 2 to 5 GeV are discussed

Supersymmetry without hermiticity

A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian. The formalism admits vanishing Witten index.Comment: 14 pages, Latex, submitted to Phys. Lett.

Pomaknuti 1/n razvoj i ograničeni kvantni sistemi

A modified version of the shifted 1/N expansion method is formulated for constrained quantum mechanical system. This method is applied to boxed-in hydrogen atom and spherical harmonic oscillator. Results from the shifted 1/N expansion method are compared with the exact numerical results in case of hydrogen atom, and with approximate analytical results in case of the spherical harmonic oscillator. Agreement between the results is found to be good in both the cases.Za ograničene kvantno mehaničke sisteme formulirana je modificirana verzija pomaknutog 1/N razvoja. Metoda je primjenjena na vodikov atom i sferni harmonički oscilator koji se nalazi u kutiji. Rezultati pomaknutog 1/N razvoja uspoređeni su s egzaktnim numeričkim rezultatima za vodikov atom, te približnim analitičkim rezultatima za sferni harmonički oscilator. Slaganje rezultata je dobro u oba slučaja