Efficient Diagonalisation of Bogoliubov deGennes Equation on Large Grids

  • Thread starter ayankhan
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In summary, the conversation between colleagues Ayan and the other person involves discussing Ayan's work on diagonalising the Bogoliubov deGennes equation using FORTRAN90 and the lapack subroutine zheevx. Ayan is facing difficulties when using a grid size beyond 51x51, and plans to resolve the hamiltonian on a 101x101 grid, resulting in a BDG matrix of 202x202. The other person suggests using Mathematica for faster computation.
  • #1
ayankhan
2
0
Dear Colleagues,
My work is related to the diagonalisation of Bogoliubov deGennes (BDG) equation.
But numerically it is becomming very tough when I go beyond 51[tex]\times[/tex] 51 grid.
I am working in fortran90 and using lapack subroutine (zheevx) for diagonalisation. The matrix is not sparse.
regards
ayan
 
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  • #2
ayankhan said:
Dear Colleagues,
My work is related to the diagonalisation of Bogoliubov deGennes (BDG) equation.
But numerically it is becomming very tough when I go beyond 51[tex]\times[/tex] 51 grid.
I am working in fortran90 and using lapack subroutine (zheevx) for diagonalisation. The matrix is not sparse.
regards
ayan

and what is your question? ;P

oh, okay, the question is implied. So, how big is the matrix you are diagonalizing?
 
  • #3
I want to resolve the hamiltonian in 101\times101 grid. which means the BDG matrix will be of 202\times202.
regards
ayan
 
  • #4
ayankhan said:
I want to resolve the hamiltonian in 101\times101 grid. which means the BDG matrix will be of 202\times202.
regards
ayan

That's not very big... What seems to be the problem? In fact this is small enough that you should be able to do it with Mathematica very quickly I think.
 

FAQ: Efficient Diagonalisation of Bogoliubov deGennes Equation on Large Grids

1. What is the Bogoliubov deGennes Equation?

The Bogoliubov deGennes Equation is a mathematical equation used to describe the behavior of superconductors. It was developed by theoretical physicists Nikolay Bogoliubov and Alexander deGennes in the 1950s.

2. How does the equation work?

The equation describes the behavior of particles in a superconductor by taking into account the effects of quantum mechanics and the interactions between particles. It is a partial differential equation that can be used to calculate the energy levels and wave functions of particles in a superconductor.

3. What are the applications of this equation?

The Bogoliubov deGennes Equation has many applications in the field of superconductivity. It can be used to understand the properties of superconductors, such as the critical temperature at which they become superconducting and the behavior of vortices within the material. It is also used in the development of new superconducting materials and technologies.

4. Is the equation accurate?

The Bogoliubov deGennes Equation has been extensively tested and has been shown to accurately describe the behavior of superconductors. However, like any mathematical model, it is an approximation and may not fully capture all aspects of a real system. Researchers continue to refine and improve the equation to make it more accurate.

5. Are there any limitations to this equation?

While the Bogoliubov deGennes Equation is a powerful tool for understanding superconductors, it does have limitations. It does not take into account certain factors, such as impurities or disorder within the superconductor, which can affect its accuracy. Additionally, the equation may not be applicable to all types of superconductors, as some may exhibit behaviors that cannot be described by this equation.

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