We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable on-site- and intersite-centered semidiscrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to five, in both tightly bound and quasicontinuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semidiscrete vortex QDs, including ones with multiple vorticity.
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http://dx.doi.org/10.1103/PhysRevLett.123.133901 | DOI Listing |
Entropy (Basel)
February 2024
Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile.
This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
View Article and Find Full Text PDFR Soc Open Sci
November 2020
Institut za nuklearne nauke Vinča, Univerzitet u Beogradu, 11001 Beograd, Serbia.
The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA.
View Article and Find Full Text PDFPhys Rev E
January 2020
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Absorbing boundary conditions are presented for three-dimensional time-dependent Schrödinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a semidiscrete approximation of the Schrödinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing boundary condition is expressed as a discrete Dirichlet-to-Neumann map, which can be further approximated in time by using rational approximations of the Laplace transform to enable a more efficient implementation.
View Article and Find Full Text PDFPhys Rev Lett
September 2019
School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China.
Chaos
October 2016
Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers' Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon.
We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI.
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