The storm before the calm?
We are very close to the end!
I need certain things to click. As I have come to learn, cracking the algorithmic part is a small part of the coding job. A code that produces accurate results have to withstand iterations of scrutiny, examination and cross-examination before it is given the green light. But, for me, the cracking part is the most crucial part. The project/functionality is made possible because an accurate code was produced, however 'unclean' and unscrutable. Everything hinges on that first breakthrough. I had to go over all the mathematics of Branch cuts in logarithmic functions to write a unfailing Chern number calculation routine.
The most important functionality I want to add is the Chern number calculator function. This is not a simple calculation that can be done with any brute force way. It involves a intimate knowledge of branch cut of complex Logarithmic functions and also highlights the Gauge dependency of quantities in a Quantum problem.
I am having some difficulty in calculating the line intergral of the Berry connection, which invariably is coming out to be zero in my calculations. But the surface integral of the curl of the Berry connection works like a charm in getting the right Berry phase and Chern number.
I am going to come back to this post and figure out if I can resolve this problem. For that and to learn how the dust settled, stay tuned!
PS. We are also contemplating some fun problems with the Caldeira Leggett model.
I need certain things to click. As I have come to learn, cracking the algorithmic part is a small part of the coding job. A code that produces accurate results have to withstand iterations of scrutiny, examination and cross-examination before it is given the green light. But, for me, the cracking part is the most crucial part. The project/functionality is made possible because an accurate code was produced, however 'unclean' and unscrutable. Everything hinges on that first breakthrough. I had to go over all the mathematics of Branch cuts in logarithmic functions to write a unfailing Chern number calculation routine.
The most important functionality I want to add is the Chern number calculator function. This is not a simple calculation that can be done with any brute force way. It involves a intimate knowledge of branch cut of complex Logarithmic functions and also highlights the Gauge dependency of quantities in a Quantum problem.
I am having some difficulty in calculating the line intergral of the Berry connection, which invariably is coming out to be zero in my calculations. But the surface integral of the curl of the Berry connection works like a charm in getting the right Berry phase and Chern number.
I am going to come back to this post and figure out if I can resolve this problem. For that and to learn how the dust settled, stay tuned!
PS. We are also contemplating some fun problems with the Caldeira Leggett model.
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