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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physica A: Statistical Mechanics and its Applications 167 (1990), S. 66-92 
    ISSN: 0378-4371
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physica B: Physics of Condensed Matter 169 (1991), S. 491-492 
    ISSN: 0921-4526
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 7 (1999), S. 451-456 
    ISSN: 1434-6036
    Keywords: PACS. 05.45.+b Theory and models of chaotic systems - 72.15.Rn Quantum localization - 71.30.+h Metal-insulator transitions and other electronic transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 1 (1998), S. 223-227 
    ISSN: 1434-6036
    Keywords: PACS. 72.15.-vElectronic conduction in metals and alloys[:AND:] 73.20.-rSurface and interface electron states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock states is shown to decrease the mobility in metals and to increase it in insulators. In contrast to the single particle case, the spectral rigidity is not directly related to the level curvature. Therefore, another curvature of topological origin is introduced, which defines the energy scale below which the spectrum has the universal Wigner-Dyson rigidity.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 6 (1998), S. 117-121 
    ISSN: 1434-6036
    Keywords: PACS. 05.45.+b Theory and models of chaotic systems - 72.15.Rn Quantum localization - 71.30.+h Metal-insulator transitions and other electronic transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 10 (1999), S. 149-158 
    ISSN: 1434-6036
    Keywords: PACS. 71.10.-w Theories and models of many electron systems - 71.30.+h Metal-insulator transitions and other electronic transitions - 73.20.Jc Delocalization processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The interplay between the quantum interferences responsible for one particle localization over a length L1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L 2 〉 L 1 , is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t1 necessary to propagate over L1, the interaction slows down the ballistic motion. On the contrary, after t1 the interaction favors a very slow delocalization, characterized by a spreading of the center of mass, until L2 is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 30 (2002), S. 93-100 
    ISSN: 1434-6036
    Keywords: PACS. 71.10.-w Theories and models for many-electron systems – 71.27.+a Strongly correlated electron systems – 73.20.Qt Electron solids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L 0 = π2(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L 0, up to finite size corrections of order L-2. L 〈 L 0 and L 〉 L 0 are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U *(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 31 (2003), S. 401-412 
    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
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 33 (2003), S. 87-101 
    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
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  • 10
    ISSN: 1434-6036
    Keywords: PACS. 71.30.+h Metal-insulator transitions and other electronic transitions - 72.15.Rn Localization effects (Anderson or weak localization)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L 2 towards a 1/L decay when the Coulomb energy to Fermi energy ratio increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at .
    Type of Medium: Electronic Resource
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