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  • Electronic Resource  (9)
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  • 2003  (9)
  • TP13  (3)
  • 74B20  (2)
  • PACS. 71.10.-w Theories and models of many-electron systems – 73.21.La Quantum dots – 73.20.Qt Electron solids  (2)
  • PACS. 71.35.-y Excitons and related phenomena  (2)
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  • Electronic Resource  (9)
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  • 2010-2014
  • 2005-2009
  • 2000-2004  (9)
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  • 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
    Density expansion of the energy of N close-to-boson excitons (2003)
    Springer
    The European physical journal 31 (2003), S. 517-523 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 71.35.-y Excitons and related phenomena
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na x 3/ )n with n ≥ 2. An exact procedure to get these density dependent terms is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjb/e2003-00061-3
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  • 3
    Electronic Resource
    Electronic Resource
    Trions in first and second quantizations (2003)
    Springer
    The European physical journal 33 (2003), S. 311-320 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 71.35.-y Excitons and related phenomena
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We reconsider the semiconductor trions from scratch. We first determine the very many “reasonable” ways to write the trions in first quantization. We then select the forms which are easy to relate to physical pictures. In a second part, we derive the corresponding creation operators in second quantization. We pay particular attention to the expression of the X- trion in terms of exciton and free-electron, as it is the one adapted to future works on many-body effects with trions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjb/e2003-00171-x
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (III)—Multiple time-delay case (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1063-1074 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; controllable set ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    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 controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437638
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (II)—Single time-delay case (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1051-1062 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; controllable set ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    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 controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the oneperiodic, multiple-periodic controllability of periodic-type systems and controllability of periodic systems are presented, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437637
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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (I)—Basic properties and preliminary results (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1041-1050 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; generalized cyclic invariant subspace ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    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 controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437636
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