Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate |
| |
| Authors: | Denis Borisov Anastasia Golovina Ivan Veselić |
| |
| Affiliation: | 1.Department of Differential Equations, Institute of Mathematics with Computer Center, Ufa Scientific Center,Russian Academy of Sciences,Ufa,Russia;2.Faculty of Physics and Mathematics,Bashkir State Pedagogical University,Ufa,Russia;3.Faculty of Science,University of Hradec Králové,Hradec Králové,Czech Republic;4.Department of Fundamental Sciences,Bauman Moscow State Technical University,Moscow,Russia;5.Department of Mathematics,Technische Universit?t Chemnitz,Chemnitz,Germany |
| |
| 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: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
