QuantumATK Forum

QuantumATK => General Questions and Answers => Topic started by: Heinz on June 18, 2014, 17:48

Title: Relationship of MPSH eigenstate and transmission eigenstate
Post by: Heinz on June 18, 2014, 17:48

Hi,

What's the mathematical relationship of the "eigenstate" and the "transmission eigenstate" calculated by ATK? As mush as I know eigenstate is the eigenfunction of the Hamiltonian and the transmission eigenstate is the eigenfunction of the transmission matrix. But what's the formal or conceptual relation?

Moreover, when plotting eigenstates as isosurface, which iso value has to be used? Since changing the isovalue also changes the shape of the eigenstate plotted?

Hope to have some answers. Thanks in advance.

Title: Re: Relationship of MPSH eigenstate and transmission eigenstate
Post by: kstokbro on June 19, 2014, 07:26

The eigenstate function can give you the eigenstate of a projection of the full Hamiltonian, i.e. of a finite system.
The transmission eigenstate is a scattering eigenstate of the infinite Hamiltonian. The scattering eigenstate has specific boundary conditions, i.e. scattering left or right boundary conditions which means that it will match bloch states going left or right in the electrodes. The transmission eigenstate is the linear combination of scattering eigenstates, which diagonalizes the transmission matrix.
For further details also check the manual.
We will also publish a manual soon, which shows how to resolve the transmission eigenstate in MPSH states

Title: Re: Relationship of MPSH eigenstate and transmission eigenstate
Post by: Heinz on June 19, 2014, 07:42

Thanks a lot.