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  • 1
    Electronic Resource
    Electronic Resource
    Block Toeplitz matrices and the two-dimensional Coulomb gas near a wall (1991)
    Springer
    Journal of statistical physics 63 (1991), S. 1-23 
    Details
    ISSN: 1572-9613
    Keywords: Block Toeplitz matrices ; two-dimensional Coublomb gas ; conductors ; solvable models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For the two-dimensional Coulomb gas on a lattice, at the special value of the dimensionless coupling constantΓ=2, the grand partition function and correlations can be written in terms of the eigenvalues and eigenvectors of a block Toeplitz matrix. By using the semiperiodic Coulomb potential and taking the continuum limit in the periodic direction so as to have a set of parallel lines as the domain, it is shown that these eigenvalues and eigenvectors can be computed exactly. This allows the pressure and the correlations near a charged wall to be rigorously evaluated. The two-particle correlations obey a sum rule which implies that the state in the vicinity of the wall is a conductor.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01026589
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Recurrence equations for the computation of correlations in the 1/r2 quantum many-body system (1993)
    Springer
    Journal of statistical physics 72 (1993), S. 39-50 
    Details
    ISSN: 1572-9613
    Keywords: Selberg integrals ; correlation functions ; solvable models ; 1/r 2 quantum system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In a previous paper the two-particle distribution function and one-particle density matrix for the quantum many-body system with the 1/r 2 pair potential have been expressed as limiting cases of Selberg correlation integrals. Recurrence equations are derived which allow rapid evaluation of these multidimensional integrals. The exact results for the two-particle distribution are compared with the harmonic approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048039
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The two-dimensional Coulomb gas on a sphere: Exact results (1992)
    Springer
    Journal of statistical physics 69 (1992), S. 179-192 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb gas ; solvable models ; Dirac equation ; curved space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract At the special value of the reduced inverse temperatureΓ=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053789
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Universality in some classical Coulomb systems of restricted dimension (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 359-378 
    Details
    ISSN: 1572-9613
    Keywords: Universality ; Coulomb systems ; finite-size effects ; solvable models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond−1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179647
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    The two-dimensional two-component plasma plus background on a sphere: Exact results (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 337-357 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb gas ; solvable models ; finite-size corrections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made up of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value Γ=2 of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179646
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    Paper (German National Licenses)
    Fulltext
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