- #1

Alena_Alena

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- TL;DR Summary
- Green's function for tunneling electrons between quantum dots

Good afternoon!

I am writing with such a problem, I hope to find someone who could help me. I'm almost desperate! So, there is such a thing as the Braess paradox, this is a classic paradox for roads and power grids, and there is also such an article (https://arxiv.org/ftp/arxiv/papers/1208/1208.0955.pdf) for the Braess quantum paradox.

My task is to simulate their experiment, but replace the mesoscopic network with a network of quantum dots. I have all rested on the Green function, I have never worked with this, I do not know how to write a Green function for my task, maybe here will be someone who will help. My teacher also did not work with Green's functions, we assumed that we could go from the opposite (not to write a function from the very beginning, but from a ready-made function to spin to the beginning, the ready-made Green's function is in this article).

The plan is to go from the opposite: 1) calculation of the Hamiltonian matrix on a two-dimensional spatial grid, 2) the Green function itself, 3) frequency integration at each node. In the article, the authors write that all modes were used, which means that we need to numerically solve the problem for the spectrum, and then construct the Green's function.

We need to set the potential of their and my structure using two-dimensional exponential-power functions. Then solve the spectrum problem. Nevertheless, it seems to me that this is not very promising, because the Green function will need to be changed for my task. For me, it all turned out to be complicated somehow.

Help me, I don't know what to do.

I am writing with such a problem, I hope to find someone who could help me. I'm almost desperate! So, there is such a thing as the Braess paradox, this is a classic paradox for roads and power grids, and there is also such an article (https://arxiv.org/ftp/arxiv/papers/1208/1208.0955.pdf) for the Braess quantum paradox.

My task is to simulate their experiment, but replace the mesoscopic network with a network of quantum dots. I have all rested on the Green function, I have never worked with this, I do not know how to write a Green function for my task, maybe here will be someone who will help. My teacher also did not work with Green's functions, we assumed that we could go from the opposite (not to write a function from the very beginning, but from a ready-made function to spin to the beginning, the ready-made Green's function is in this article).

The plan is to go from the opposite: 1) calculation of the Hamiltonian matrix on a two-dimensional spatial grid, 2) the Green function itself, 3) frequency integration at each node. In the article, the authors write that all modes were used, which means that we need to numerically solve the problem for the spectrum, and then construct the Green's function.

We need to set the potential of their and my structure using two-dimensional exponential-power functions. Then solve the spectrum problem. Nevertheless, it seems to me that this is not very promising, because the Green function will need to be changed for my task. For me, it all turned out to be complicated somehow.

Help me, I don't know what to do.

**I need the theoretical help**.
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