Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential

Ground State for the Schrödinger Operator with the Weighted Hardy Potential

Spectral and Localization Properties for the One-dimensional Bernoulli Discrete Dirac Operator

A 1D Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schrödinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for all values of the mass, it is shown that its spectrum is pure point, whereas the zero mass case presents dynamical delocalization for specific values of the ene...

On the Number of Eigenvalues of the Discrete One-dimensional Dirac Operator with a Complex Potential

In this paper we define a one-dimensional discrete Dirac operator on Z. We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

On the Number of Eigenvalues of the Discrete One-dimensional Schrödinger Operator with a Complex Potential

We study the eigenvalues of the discrete Schrödinger operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

Solitons in Nonlinear Schrödinger Model and the Collective Ground State of One-dimensional Delta-function Gas

We examine one-dimensional Bose gas interacting with delta-function potential using the large-N collective field theory. We show that in the case of attractive potential the uniform ground state is unstable to small perturbations and the instability is cured by formation of a collective ground state, “bright soliton” configuration in corresponding nonlinear Schrödinger field theory. Research Fe...