38 research outputs found
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