Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate
Analysis of PDEs
2016-01-15 v1 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.1501.06503,
title = {Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate},
author = {Denis Borisov and Anastasia Golovina and Ivan Veselic},
journal= {arXiv preprint arXiv:1501.06503},
year = {2016}
}