Denis Borisov, Anastasia Golovina, Ivan Veselić: Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate

Author(s):

Denis Borisov
Anastasia Golovina
Ivan Veselić

Title:

Denis Borisov, Anastasia Golovina, Ivan Veselić: Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 02, 2015

Mathematics Subject Classification:

    60H25 []
    35J10 []

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.

Keywords:

Language:

English

Publication time:

01/2015