TY - JOUR

T1 - Spectral statistics and dynamics of lévy matrices

AU - Araujo, Mariela

AU - Medina, Ernesto

AU - Aponte, Eduardo

PY - 1999

Y1 - 1999

N2 - We study the spectral statistics and dynamics of a random matrix model where matrix elements are taken from power-law tailed distributions. Such distributions, labeled by a parameter [Formula Presented] converge on the Lévy basin, giving the matrix model the label “Lévy matrix” [P. Cizeau and J. P. Bouchaud, Phys. Rev. E [Formula Presented] 1810 (1994)]. Such matrices are interesting because their properties go beyond the Gaussian universality class and they model many physically relevant systems such as spin glasses with dipolar or Ruderman-Kittel-Kasuya-Yosida interactions, electronic systems with power-law decaying interactions, and the spectral behavior at the metal insulator transition. Regarding the density of states we extend previous work to reveal the sparse matrix limit as [Formula Presented] Furthermore, we find for [Formula Presented] Lévy matrices that geometrical level repulsion is not affected by the distribution’s broadness. Nevertheless, essential singularities particular to Lévy distributions for small arguments break geometrical repulsion and make it [Formula Presented] dependent. Level dynamics as a function of a symmetry breaking parameter gives new insight into the phases found by Cizeau and Bouchaud (CB). We map the phase diagram drawn qualitatively by CB by using the [Formula Presented] statistic. Finally we compute the conductance of each phase by using the Thouless formula, and find that the mixed phase separating conducting and insulating phases has a unique character.

AB - We study the spectral statistics and dynamics of a random matrix model where matrix elements are taken from power-law tailed distributions. Such distributions, labeled by a parameter [Formula Presented] converge on the Lévy basin, giving the matrix model the label “Lévy matrix” [P. Cizeau and J. P. Bouchaud, Phys. Rev. E [Formula Presented] 1810 (1994)]. Such matrices are interesting because their properties go beyond the Gaussian universality class and they model many physically relevant systems such as spin glasses with dipolar or Ruderman-Kittel-Kasuya-Yosida interactions, electronic systems with power-law decaying interactions, and the spectral behavior at the metal insulator transition. Regarding the density of states we extend previous work to reveal the sparse matrix limit as [Formula Presented] Furthermore, we find for [Formula Presented] Lévy matrices that geometrical level repulsion is not affected by the distribution’s broadness. Nevertheless, essential singularities particular to Lévy distributions for small arguments break geometrical repulsion and make it [Formula Presented] dependent. Level dynamics as a function of a symmetry breaking parameter gives new insight into the phases found by Cizeau and Bouchaud (CB). We map the phase diagram drawn qualitatively by CB by using the [Formula Presented] statistic. Finally we compute the conductance of each phase by using the Thouless formula, and find that the mixed phase separating conducting and insulating phases has a unique character.

UR - http://www.scopus.com/inward/record.url?scp=0039158616&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.60.3580

DO - 10.1103/PhysRevE.60.3580

M3 - Artículo

AN - SCOPUS:0039158616

SN - 1063-651X

VL - 60

SP - 3580

EP - 3588

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 4

ER -