Enhancement of Persistent Currents by Hubbard Interactions In Disordered 1D Rings: Avoided Level Crossings Interpretation

We study effects of local electron interactions on the persistent current of one dimensional disordered rings. For different realizations of disorder we compute the current as a function of Aharonov-Bohm flux to zeroth and first orders in the Hubbard interaction. We find that the persistent current is {\em enhanced} by onsite interactions. Using an avoided level crossings approach, we derive analytic formulas which explain the numerical results at weak disorder. The same approach also explains the opposite effect (suppression) found for spinless fermion models with intersite interactions.Comment: uuencoded: 17 pages, text in revtex, 7 figs in postscrip

Kohn-Sham equations with functionals from the strictly-correlated regime: Investigation with a spectral renormalization method

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory (DFT), with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so-called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation (ISI) functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential

Constant-intensity waves and their modulation instability in non-Hermitian potentials

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole new class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study, for the first time, the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.Comment: 25 pages (including methods section), 4 figures; to appear in Nature Communication

Wave dynamics in optically modulated waveguide arrays

A model describing wave propagation in optically modulated waveguide arrays is proposed. In the weakly guided regime, a two-dimensional semidiscrete nonlinear Schrodinger equation with the addition of a bulk diffraction term and an external optical trap is derived from first principles, i.e., Maxwell equations. When the nonlinearity is of the defocusing type, a family of unstaggered localized modes are numerically constructed. It is shown that the equation with an induced potential is well-posed and gives rise to localized dynamically stable nonlinear modes. The derived model is of the Gross-Pitaevskii type, a nonlinear Schrodinger equation with a linear optical potential, which also models Bose-Einstein condensates in a magnetic trap

Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities

We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a two-element discretized version of this PT nonlinear Schr\"odinger equation. By obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself

Fundamental and vortex solitons in a two-dimensional optical lattice

Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and vortex solitons spread over many lattice sites. We further show that fundamental and vortex solitons are stable against small perturbations in the strong localization regime.Comment: 3 pages, 4 figure

Continuous and discrete Schrodinger systems with parity-time-symmetric nonlinearities

We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a discretized version of this PT-nonlinear Schrodinger equation on a lattice. When only two elements are involved, by obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry-breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself