A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

(AmBn)x copolymers: A computational study of electronic and excitonic properties of quasi-one-dimensional superlattices

Periodic copolymers representing quasi-one-dimensional superlattices (AmBn)x have been studied within the tight-binding approximation. The linear-combination-of-atomic-orbitals (LCAO) approach was used to calculate the splitting into subbands, the widths of the subbands, and the number of subbands in the well as a function of segment lengths m and n (barrier and well width). The Stark shift of subbands and the perturbed Wannier functions for a (A16B32)x superlattice have been calculated for various electric field strengths using perturbation theory. Exciton resonances and the shift in exciton excitation energies due to an applied electric field have been computed by using a Pariser-Parr-Pople parameter for the electron-hole interaction. The parameters for the empirical tight-binding calculations were determined from fully self-consistent Hartree-Fock calculations and first-principles Greens function calculations for the exciton energies for superlattices of shorter segment lengths. For the Stark shift of the exciton peak a red shift of 25 meV for 2×105 V/cm is calculated, similar to the shifts calculated and observed in three-dimensional superlattices. © 1988 The American Physical Society