Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems

Limit Periodic Jacobi Matrices with a Singular Continuous Spectrum and the Renormalization of Periodic Matrices

For all hyperbolic polynomials we proved in [11] a Lipschitz estimate of Jacobi matrices built by orthogonalizing polynomials with respect to measures in the orbit of classical Perron-Frobenius-Ruelle operators associated to hyperbolic polynomial dynamics (with real Julia set). Here we prove that for all sufficiently hyperbolic polynomials this estimate becomes exponentially better when the dim...

Crossover from Diffusive to Ballistic Transport in Periodic Quantum Maps

We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, t, and Planck’s constant, ~, and allows a study of both the long time, t → ∞, and semi-classical, ~ → 0, limits taken in either order. We evaluate the expression using random matrix theory as well as numerical...

Marchenko-Ostrovski mappings for periodic Jacobi matrices

We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on the quasimomentum domain . Furthermore, we obtain a priori two-sided estimates for vertical slits in terms of Jacoby matrices.

Two modified Jacobi methods for M-matrices

Quantum Many–Body Problems and Perturbation Theory

We show that the existence of algebraic forms of exactly-solvable A−B− C−D and G2, F4 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure algebraic means. A classification of perturbations leading to such a perturbation theory based on representation theory of Lie algebras is given. In particular, this scheme admits an ex...