Discussion Overview
The discussion centers on the challenges associated with the diagonalization of the Bogoliubov deGennes (BDG) equation, particularly when working with larger grid sizes in numerical simulations. The focus is on the computational difficulties encountered when moving beyond a 51×51 grid, with specific reference to the use of Fortran90 and LAPACK subroutines.
Discussion Character
- Technical explanation, Debate/contested
Main Points Raised
- One participant, Ayan, reports difficulties in diagonalizing the BDG equation for grids larger than 51×51, indicating that the matrix involved is not sparse.
- Ayan expresses a desire to resolve the Hamiltonian on a 101×101 grid, resulting in a 202×202 matrix.
- Another participant questions the significance of the matrix size, suggesting that a 202×202 matrix should be manageable and proposes that it could be handled quickly using Mathematica.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the challenges posed by the matrix size, with one participant questioning the difficulty while another expresses concern over computational feasibility.
Contextual Notes
There are no explicit limitations or assumptions noted, but the discussion reflects varying perspectives on the computational challenges associated with matrix size in numerical diagonalization.
Who May Find This Useful
Researchers and practitioners working on numerical methods for quantum mechanics, particularly those dealing with the Bogoliubov deGennes equation or similar computational challenges in large matrix diagonalization.