2,795 research outputs found
Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates
We propose an integrable model of a multicomponent spinor Bose-Einstein
condensate in one dimension, which allows an exact description of the dynamics
of bright solitons with spin degrees of freedom. We consider specifically an
atomic condensate in the F=1 hyperfine state confined by an optical dipole
trap. When the mean-field interaction is attractive (c_0 < 0) and the
spin-exchange interaction of a spinor condensate is ferromagnetic (c_2 < 0), we
prove that the system possesses a completely integrable point leading to the
existence of multiple bright solitons. By applying results from the inverse
scattering method, we analyze a collision law for two-soliton solutions and
find that the dynamics can be explained in terms of the spin precession.Comment: 4 pages, 2 figure
Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations
We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type
equations, which were shown by Olver and Sokolov to possess a higher symmetry.
We prove that two of them are `C-integrable' and the rest of them are
`S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem
Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability
The integrability of a system of two symmetrically coupled higher-order
nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by
means of the singularity analysis. It is proven that the system passes the
Painlev\'{e} test for integrability only in ten distinct cases, of which two
are new. For one of the new cases, a Lax pair and a multi-field generalization
are obtained; for the other one, the equations of the system are uncoupled by a
nonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in
J.Phys.A:Math.Ge
A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion
We propose a new method for discretizing the time variable in integrable
lattice systems while maintaining the locality of the equations of motion. The
method is based on the zero-curvature (Lax pair) representation and the
lowest-order "conservation laws". In contrast to the pioneering work of
Ablowitz and Ladik, our method allows the auxiliary dependent variables
appearing in the stage of time discretization to be expressed locally in terms
of the original dependent variables. The time-discretized lattice systems have
the same set of conserved quantities and the same structures of the solutions
as the continuous-time lattice systems; only the time evolution of the
parameters in the solutions that correspond to the angle variables is
discretized. The effectiveness of our method is illustrated using examples such
as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the
Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger
system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice
and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction
One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schr\"odinger Equation and Solution of Bogoliubov Equation in These Systems
In this short note, we construct mappings from one-dimensional integrable
spinor BECs to matrix nonlinear Schr\"odinger equation, and solve the
Bogoliubov equation of these systems. A map of spin- BEC is constructed from
the -dimensional spinor representation of irreducible tensor operators of
. Solutions of Bogoliubov equation are obtained with the aid of the
theory of squared Jost functions.Comment: 2.1 pages, JPSJ shortnote style. Published version. Note and
reference adde
Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations
We present a simple and efficient technique in ab initio electronic-structure
calculation utilizing real-space double-grid with a high density of grid points
in the vicinity of nuclei. This technique promises to greatly reduce the
overhead for performing the integrals that involves non-local parts of
pseudopotentials, with keeping a high degree of accuracy. Our procedure gives
rise to no Pulay forces, unlike other real-space methods using adaptive
coordinates. Moreover, we demonstrate the potential power of the method by
calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
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Genomic signatures of heterokaryosis in the oomycete pathogen Bremia lactucae.
Lettuce downy mildew caused by Bremia lactucae is the most important disease of lettuce globally. This oomycete is highly variable and rapidly overcomes resistance genes and fungicides. The use of multiple read types results in a high-quality, near-chromosome-scale, consensus assembly. Flow cytometry plus resequencing of 30 field isolates, 37 sexual offspring, and 19 asexual derivatives from single multinucleate sporangia demonstrates a high incidence of heterokaryosis in B. lactucae. Heterokaryosis has phenotypic consequences on fitness that may include an increased sporulation rate and qualitative differences in virulence. Therefore, selection should be considered as acting on a population of nuclei within coenocytic mycelia. This provides evolutionary flexibility to the pathogen enabling rapid adaptation to different repertoires of host resistance genes and other challenges. The advantages of asexual persistence of heterokaryons may have been one of the drivers of selection that resulted in the loss of uninucleate zoospores in multiple downy mildews
Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates
We study soliton solutions for the Gross--Pitaevskii equation of the spinor
Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses
are made in two ways: by assuming single-mode amplitudes and by generalizing
Hirota's direct method for multi-components. We obtain one-solitons of
single-peak type in the ferromagnetic, polar and cyclic states, respectively.
Moreover, twin-peak type solitons both in the ferromagnetic and the polar state
are found.Comment: 15 pages, 8 figure
Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method
We use the effective-mass approximation and the density-functional theory
with the local-density approximation for modeling two-dimensional
nano-structures connected phase-coherently to two infinite leads. Using the
non-equilibrium Green's function method the electron density and the current
are calculated under a bias voltage. The problem of solving for the Green's
functions numerically is formulated using the finite-element method (FEM). The
Green's functions have non-reflecting open boundary conditions to take care of
the infinite size of the system. We show how these boundary conditions are
formulated in the FEM. The scheme is tested by calculating transmission
probabilities for simple model potentials. The potential of the scheme is
demonstrated by determining non-linear current-voltage behaviors of resonant
tunneling structures.Comment: 13 pages,15 figure
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