A transfer matrix method for the analysis of fractal quantum

In summary, the conversation revolved around a project involving the use of the transfer matrix method in quantum tunneling using MATLAB. The person was seeking guidance on how to generate functions for calculating eigenvalues and representing the transmission coefficient. They were advised to use the built-in "eig" function for calculating eigenvalues and the "plot" function for representing the transmission coefficient. Additional resources such as documentation, tutorials, and online forums were also suggested for further assistance.
  • #1
Good day, guys !

I am working on a project regarding the transfer matrix method used in quantum tunneling by means of a MATLAB program --- Cantor set fractal potentials. I am trying to represent some things here (as seen in the document below) :

- the eigenvalues for the energy
- the representation for the transmission coefficient

The only problem is, as a beginner in MATLAB, I do not know how to generate such a function. Some indication would be great.
The document for this is here (obviously without the program :D) :
http://iopscience.iop.org/0143-0807/26/4/005/

Thank you !
Have a pleasant day !
 
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  • #2

Thank you for sharing your project with us. It sounds very interesting and challenging. I have some experience with MATLAB and I would be happy to provide some guidance on how to generate the functions you need.

To generate the eigenvalues for the energy, you can use the built-in function "eig". This function calculates the eigenvalues of a given matrix. In your case, you will need to create a matrix representing the transfer matrix method and then use the "eig" function to calculate the eigenvalues.

For the representation of the transmission coefficient, you can use the "plot" function in MATLAB. This function allows you to plot different types of graphs, including line graphs, scatter plots, and histograms. You can use this function to plot the transmission coefficient values against the energy levels.

I would also recommend checking out MATLAB's documentation and tutorials for more information on how to use the "eig" and "plot" functions. You can also find helpful tips and examples on online forums and communities dedicated to MATLAB.

I hope this helps you get started with your project. Good luck and have a pleasant day!
 

What is a transfer matrix method?

A transfer matrix method is a mathematical tool used to analyze the properties of fractal quantum systems. It involves breaking down a fractal system into smaller segments and using a matrix to represent the relationship between each segment.

How does the transfer matrix method work?

The transfer matrix method works by representing the fractal system as a series of matrices, each representing the relationship between neighboring segments. By multiplying these matrices together, the overall transfer matrix can be obtained, which contains information about the properties of the fractal system.

What are the advantages of using the transfer matrix method for fractal quantum analysis?

The transfer matrix method allows for a more efficient and accurate analysis of fractal quantum systems compared to other methods. It also provides a deeper understanding of the properties of fractals, such as their self-similarity and scaling behavior.

Can the transfer matrix method be applied to any type of fractal system?

Yes, the transfer matrix method can be applied to any type of fractal system, as long as it can be broken down into smaller segments and the relationship between these segments can be represented by a matrix.

What are the potential applications of the transfer matrix method in quantum physics?

The transfer matrix method has potential applications in various areas of quantum physics, including the study of quantum transport, quantum chaos, and the behavior of quantum systems at different energy scales. It can also be used to analyze and design new types of quantum devices and materials.

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