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  • 1
    Digitale Medien
    Digitale Medien
    On the average distance between particles in the two-dimensional two-component plasma (1992)
    Springer
    Journal of statistical physics 69 (1992), S. 163-178 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Two-component plasma ; Kosterlitz-Thouless transition ; exact solution
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The asymptotic forms of the average distance of the closest particle to a fixed positive charge, and of the closest particle to the origin, are obtained for the two-dimensional two-component plasma in the low-density limit. The asymptotic forms of the average areas of the corresponding disks formed by the closest particle are also derived. These results are verified at a special coupling where exact results are available.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01053788
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  • 2
    Digitale Medien
    Digitale Medien
    Properties of an exact crystalline many-body ground state (1994)
    Springer
    Journal of statistical physics 76 (1994), S. 331-346 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Wigner solid ; Jastrow-type wave function ; correlation functions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A new quantum many-body Hamiltonian is introduced, for which the exact ground state is a Jastrow-type product. This Hamiltonian is interpreted as a one-component |x|-potential Coulomb system in free boundary conditions, and by explicit calculation it is shown that the ground state is crystalline. The generaln-body density matrix is calculated, and is related to then-body density matrix calculated in periodic boundary conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02188665
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  • 3
    Digitale Medien
    Digitale Medien
    Exact results for correlations in a two-component log-gas (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 57-79 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Insulator-conductor phase transition ; two-component plasma ; exact solution
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A study of the one-dimensional lattice gas of positive and negative charges interacting via the logarithmic potential is continued. The two-particle distribution functions are evaluated exactly at the couplingsΓ=2 and 4. It is proved that theΓ=4 isotherm exhibits an insulator-conductor phase transition at the reduced density 1/2, and the scaling behavior of the correlations near this critical point is given. Similarities of the conjectured phase diagram with that of a one-dimensional one-component log-gas in a periodic potential are noted.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01023473
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Selberg integrals ; correlation functions ; solvable models ; 1/r 2 quantum system
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01048039
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  • 5
    Digitale Medien
    Digitale Medien
    A testbench for the nested dipole hypothesis of Kosterlitz and Thouless (1995)
    Springer
    Journal of statistical physics 79 (1995), S. 503-523 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Kosterlitz-Thouless transition ; Coulomb gas ; renormalization equations ; correlations ; exact solution
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02184869
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  • 6
    Digitale Medien
    Digitale Medien
    Classical Skew Orthogonal Polynomials and Random Matrices (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 141-170 
    Details
    ISSN: 1572-9613
    Schlagwort(e): random matrices ; correlation functions ; orthogonal polynomials
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Skew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the case that the eigenvalue probability density function involves a classical weight function, explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials, and the structure is used to give a closed-form expression for the sum. This theory treates all classical cases on an equal footing, giving formulas applicable at once to the Hermite, Laguerre, and Jacobi cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018644606835
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