Modeling a Quantum Hall System via Elliptic Equations

Figure 1

A numerical solution of (4.1) with 𝐸=5 (in units adopted throughout the paper), 𝑅_𝐻=3/5, and 𝐴₂≡0. The initial values 𝜓₂(𝑥,0)=0.3exp(𝑖𝑥)+0.2∗exp(2𝑖𝑥),𝜓₁(𝑥,0)=−0.9𝜓₂(𝑥,0), and 𝐴₁(𝑥,0)=0 are prescribed on the edge facing front right.

(a)

(b)

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