Discussion Overview
The discussion revolves around the characteristics of Wannier-Stark states in tilted lattices, focusing on their localization, stability, and methods for calculation. Participants explore theoretical aspects, numerical approaches, and references to existing literature.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant suggests that Wannier-Stark states should be extended due to the lack of a lower bound in the potential.
- Another participant asserts that when the electric field is strong, the Wannier state is localized and refers to M. Dignam's article for support.
- Some participants describe Wannier-Stark states as quasi-stable and resonant states, questioning the reasons behind their quasi-stability.
- A participant mentions using a tight-binding model and numerical diagonalization of the Hamiltonian to find well-localized eigenstates, except near the boundaries.
- It is noted that in a one-dimensional tight-binding lattice without interband tunneling, the Wannier-Stark state is a rigorously localized state with equidistant eigenenergy levels.
- Conversely, if interband tunneling is present, the Wannier-Stark state becomes a resonant state and is considered quasi-stable.
- Another participant points out the distinction between Wannier states and Wannier-Stark states, requesting further clarification.
Areas of Agreement / Disagreement
Participants express differing views on the localization and stability of Wannier-Stark states, with some asserting localization under strong electric fields while others propose that they are extended. The discussion remains unresolved regarding the nature of these states and their stability.
Contextual Notes
There are limitations in the discussion regarding assumptions about the potential landscape, the effects of interband tunneling, and the specific conditions under which the states are analyzed. The mathematical steps involved in the calculations are not fully detailed.