Journal: Mathematical Physics, Analysis and Geometry

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Springer

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1385-0172
1572-9656

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Publications 1 - 4 of 4
  • Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities
    Item type: Journal Article
    Lemm, Marius; Sutter, David (2022)
    Mathematical Physics, Analysis and Geometry
    Lyapunov exponents characterize the asymptotic behavior of long matrix products. In this work we introduce a new technique that yields quantitative lower bounds on the top Lyapunov exponent in terms of an efficiently computable matrix sum in ergodic situations. Our approach rests on two results from matrix analysis-the n-matrix extension of the Golden-Thompson inequality and an effective version of the Avalanche Principle. While applications of this method are currently restricted to uniformly hyperbolic cocycles, we include specific examples of ergodic Schrodinger cocycles of polymer type for which outside of the spectrum our bounds are substantially stronger than the standard Combes-Thomas estimates. We also show that these techniques yield short proofs of quantitative stability results for the top Lyapunov exponent which are known from more dynamical approaches. We also discuss the problem of finding stable bounds on the Lyapunov exponent for almost-commuting matrices.
  • Thermal ionization
    Item type: Journal Article
    Fröhlich, Jürg; Merkli, Marco (2004)
    Mathematical Physics, Analysis and Geometry
  • Stability of the Classical Catenoid and Darboux–Pöschl–Teller Potentials
    Item type: Journal Article
    Hoppe, Jens; Moosavi, Per (2022)
    Mathematical Physics, Analysis and Geometry
    We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schrödinger operator with an asymmetric Darboux–Pöschl–Teller potential.
  • Finite-size Energy of Non-interacting Fermi Gases
    Item type: Journal Article
    Gebert, Martin (2015)
    Mathematical Physics, Analysis and Geometry
Publications 1 - 4 of 4