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  • 1
    Electronic Resource
    Electronic Resource
    Density and correlation functions for the two-component plasma at Γ=2 near a metal wall (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 4545-4549 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The density profiles and correlation functions are computed exactly, at the special coupling Γ=2, for the two-dimensional two-component plasma separated by an impermeable membrane of width ε from a metal wall. In a grand canonical formalism, the Hamiltonian used includes the image forces due to the metal wall. This provides a direct calculation of results obtained previously as a limiting case of the ideally polarizable interface [F. Cornu and B. Jancovici, J. Chem. Phys. 90, 2444 (1989)], and extends those results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461745
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  • 2
    Electronic Resource
    Electronic Resource
    Complex Wishart matrices and conductance in mesoscopic systems: Exact results (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6736-6747 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is noted that the hypothesis of independent random complex elements for the off diagonal blocks (say, M2 and M3) of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product M3°M3 (or M2°M2) to be computed exactly. Exact expressions, in terms of double Wronskian and Toeplitz determinants, are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530639
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  • 3
    Electronic Resource
    Electronic Resource
    Exact calculation of the ground-state single-particle Green's function for the 1/r2 quantum many-body system at integer coupling (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 86-96 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The ground-state single-particle Green's function describing hole propagation is calculated exactly for the 1/r2 quantum many-body system at integer coupling. The result is in agreement with a recent conjecture of Haldane. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531328
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  • 4
    Electronic Resource
    Electronic Resource
    Exact results and universal asymptotics in the Laguerre random matrix ensemble (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2539-2551 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For various values of the parameters in the Laguerre random matrix ensemble, the distribution of the smallest eigenvalue and the scaled n-level distribution function are calculated exactly in terms of generalized hypergeometric functions. In certain cases these functions are expressed as multidimensional integrals, from which asymptotic formulas are calculated and predictions of universal behavior verified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530883
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  • 5
    Electronic Resource
    Electronic Resource
    The ideally polarizable interface: The metallic boundary limit (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 2366-2367 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The model of a classical one-component plasma in the vicinity of a metallic hard wall is shown to be a limiting case of an ideally polarizable interface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449278
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  • 6
    Electronic Resource
    Electronic Resource
    Exact Wigner Surmise Type Evaluation of the Spacing Distribution in the Bulk of the Scaled Random Matrix Ensembles (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 195-200 
    Details
    ISSN: 1573-0530
    Keywords: random matrices ; Painlevé transcendents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices, respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s)e−b(s) for a simply related to a Painlevé transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011074616607
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Charged rods in a periodic background: A solvable model (1986)
    Springer
    Journal of statistical physics 42 (1986), S. 871-894 
    Details
    ISSN: 1572-9613
    Keywords: Kosterlitz-Thouless phase transition ; exact solvability ; one-component plasma
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-component Coulomb system with logarithmic potential in a periodic background is considered. In one dimension, when the background has the same period as the average interparticle spacing, the system is exactly solvable for three values of the coupling constant. The exact solution exhibits insulating-conducting phase transitions. An heuristic argument is presented which predicts the phase diagram for this system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010450
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  • 9
    Electronic Resource
    Electronic Resource
    Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases (1990)
    Springer
    Journal of statistical physics 60 (1990), S. 203-220 
    Details
    ISSN: 1572-9613
    Keywords: Conductor-insulator transition ; Yang-Lee theory ; exact solvability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity (ξ) plane at ξ=0, whereas in the insulating phase a neighborhood of ξ=0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless couplingΓ, the zeros pinch the point ξ=0 forΓ〈2, while forΓ⩾2 a neighborhood of ξ=0 is zero free. The conductor-insulator transition therefore takes place atΓ=2 independent of the density and other parameters in the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013674
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  • 10
    Electronic Resource
    Electronic Resource
    Solvable isotherms for a two-component system of charged rods on a line (1988)
    Springer
    Journal of statistical physics 51 (1988), S. 457-479 
    Details
    ISSN: 1572-9613
    Keywords: Random matrices ; quantum Brownian motion ; partition function zeros ; phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constantΓ=q 2/k B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity planeξ, all the zeros of the grand partition function lie on the negative real axis forΓ〈2, on the pointξ=−1 forΓ=2, and on the unit circle forΓ〉2. In addition, forΓ〉4, we conjecture in general and prove atΓ=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01028466
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