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Háskólinn í Reykjavík > Tæknisvið / School of Technology > BSc Tölvunarfræðideild / Department of Computer Science >

Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/41821

Titill: 
  • Titill er á ensku Breadslice and Doughnut matrix reordering bijection algorithm for Green’s function calculation
Námsstig: 
  • Bakkalár
Höfundur: 
Útdráttur: 
  • Útdráttur er á ensku

    One of the key problems in nanotechnology is to model electron density and current in a nano-wire. Typically the calculation of Green’s function plays a fundamental role in this modelling. However, whereas this computational task is relatively simple for structures like vertically sliced two-terminal nano-wire systems, it becomes computationally heavy for four terminal systems. This is due to the non-tridiagonal nature of the Hamiltonian matrix that we need to invert to calculate Green’s function. Therefore we want to rearrange the entries of the matrix to obtain tridiagonality. To this end, in this article we will introduce an algorithm to reorder a Hamiltonian matrix for a four terminal nano-structure in order to more efficiently find its inverse. This algorithm is a bijection and therefore allows for parallel mapping of elements in the Hamiltonian matrix and also allows for mapping the matrix back to its original vertically sliced form. Finding the inverse of the Hamiltonian matrix then allows for the calculation of Green’s function from which we obtain the electron density in the system and the electric current through the system from a given terminal to another.

Samþykkt: 
  • 13.6.2022
URI: 
  • http://hdl.handle.net/1946/41821


Skrár
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