Annales Henri Poincaré

, Volume 17, Issue 9, pp 2341–2377 | Cite as

Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate

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Abstract

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e., the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Denis Borisov
    • 1
    • 2
    • 3
  • Anastasia Golovina
    • 4
  • Ivan Veselić
    • 5
  1. 1.Department of Differential Equations, Institute of Mathematics with Computer Center, Ufa Scientific CenterRussian Academy of SciencesUfaRussia
  2. 2.Faculty of Physics and MathematicsBashkir State Pedagogical UniversityUfaRussia
  3. 3.Faculty of ScienceUniversity of Hradec KrálovéHradec KrálovéCzech Republic
  4. 4.Department of Fundamental SciencesBauman Moscow State Technical UniversityMoscowRussia
  5. 5.Department of MathematicsTechnische Universität ChemnitzChemnitzGermany

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