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  • Electronic Resource  (4)
  • 2000-2004  (4)
  • 1920-1924
  • 2003  (4)
  • 74B20  (2)
  • PACS. 71.10.-w Theories and models of many-electron systems – 73.21.La Quantum dots – 73.20.Qt Electron solids  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I (2003)
    Springer
    The European physical journal 31 (2003), S. 401-412 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 71.10.-w Theories and models of many-electron systems – 73.21.La Quantum dots – 73.20.Qt Electron solids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio r s = UL/(2t ) reaches a value r s F ≈ 10, there is a level crossing between ground states of different momenta. Above r s F, the mesoscopic crystallization proceeds through an intermediate regime ( r s F 〈 r s 〈 r s W ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r s F is avoided and gives rise to a lower threshold r s F(W) 〈 r s F where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjb/e2003-00048-0
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  • 2
    Electronic Resource
    Electronic Resource
    Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II (2003)
    Springer
    The European physical journal 33 (2003), S. 87-101 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 71.10.-w Theories and models of many-electron systems – 73.21.La Quantum dots – 73.20.Qt Electron solids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as rs increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjb/e2003-00145-0
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Cavity formation at the center of a sphere composed of two compressible hyper-elastic materials (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1009-1016 
    Details
    ISSN: 1573-2754
    Keywords: compressible hyper-elastic material ; cavitated bifurcation ; catastrophe and concentration of stress ; energy comparison ; O343 ; 74B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials under a uniform boundary radial stretch was examined. The solutions, including the trivial solution and the cavitated solutions, were obtained. The bifurcation curves and the stress contributions subsequent to cavitation were discussed. The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437633
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  • 4
    Electronic Resource
    Electronic Resource
    Analysis of elastic layers with dilative eigenstrains varying through the thickness (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 997-1008 
    Details
    ISSN: 1573-2754
    Keywords: eigenstrain ; elastic layer ; three-dimensional analysis ; O781 ; 74B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state-space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid-plane, which are governed by a set of two-dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two-dimensional equations immediately gives the three-dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437632
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    Paper (German National Licenses)
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