Groundstate properties of smallsize nonlinear dynamical lattices
Abstract
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and BoseEinstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the groundstate and the lowestenergy modes of such fewsite nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the singlepulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the singlepulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the groundstate (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.
 Authors:
 Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I10129 Torino (Italy)
 Department of Mathematics and Statistics, University of Massachusetts, Amherst Massachusetts 010034515 (United States)
 Dipartimento di Fisica and CNRINFM, Universita degli Studi di Parma, Parco Area delle Scienze 7/a, I43100 Parma (Italy)
 Publication Date:
 OSTI Identifier:
 21072276
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.75.016212; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; BOSEEINSTEIN CONDENSATION; COUPLING; GROUND STATES; INSTABILITY; LATTICE FIELD THEORY; MATHEMATICAL SOLUTIONS; NONLINEAR OPTICS; NONLINEAR PROBLEMS; PULSES; SCHROEDINGER EQUATION; WAVEGUIDES
Citation Formats
Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A. Groundstate properties of smallsize nonlinear dynamical lattices. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.016212.
Buonsante, P., Penna, V., Kevrekidis, P. G., & Vezzani, A. Groundstate properties of smallsize nonlinear dynamical lattices. United States. doi:10.1103/PHYSREVE.75.016212.
Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A. Mon .
"Groundstate properties of smallsize nonlinear dynamical lattices". United States.
doi:10.1103/PHYSREVE.75.016212.
@article{osti_21072276,
title = {Groundstate properties of smallsize nonlinear dynamical lattices},
author = {Buonsante, P. and Penna, V. and Kevrekidis, P. G. and Vezzani, A.},
abstractNote = {We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and BoseEinstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the groundstate and the lowestenergy modes of such fewsite nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the singlepulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the singlepulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the groundstate (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.},
doi = {10.1103/PHYSREVE.75.016212},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

We study properties of the strongly repulsive Bose gas on onedimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through BoseFermi mapping. We first exploit the phase transition of hardcore bosons in optical lattices from the superfluid to the Boseglass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the oneparticle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Ourmore »

Groundstate properties of hardcore bosons confined on onedimensional optical lattices
We study the groundstate properties of hardcore bosons trapped by arbitrary confining potentials on onedimensional optical lattices. A recently developed exact approach based on the JordanWigner transformation is used. We analyze the large distance behavior of the oneparticle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the lowdensity limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hardcore boson gas without the lattice. 
Groundstate structural and dynamical properties of solid C sub 60 from an empirical intermolecular potential
A simple intermolecular potential is constructed to describe solid C{sub 60}. The structural and elastic properties are calculated and show good agreement with available experimental results. Phonondispersion curves and density of states are predicted. The librational modes are found to be between 10 and 20 cm{sup {minus}1} and the highest vibrational mode is at 45 cm{sup {minus}1}. The phonon density of states is used to calculate the specific heat, which agrees reasonably well with experiment. 
Groundstate and dynamical properties of twodimensional dipolar Fermi liquids
We study the groundstate properties of a twodimensional spinpolarized fluid of dipolar fermions within the Euler–Lagrange Fermihypernettedchain approximation. Our method is based on the solution of a scattering Schrödinger equation for the “pair amplitude” √(g(r)), where g(r) is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow–Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree–Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range ofmore » 
Nonlinear stability and small fluctuations around a classical YangMills ground state
It is well known that a classical uniform YangMills magnetic field is unstable under small fluctuations. We study the nonlinear stability of such a system. Assuming that only the unstable modes are important, we develop an approximation method to describe the interaction among these modes. We investigate the true classical ground state of this system and obtain the frequency of small fluctuations around it.