56 lines
1.0 KiB
Python
56 lines
1.0 KiB
Python
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#! /usr/bin/env python3
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import sympy as sp
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A = sp.Matrix([[0, 0, 0], [0, 0, -1], [0, -1, 0]])
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B = sp.Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
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kx, ky = sp.symbols("kx ky")
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A = kx * A + ky * B
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print("flux")
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sp.pprint(A)
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eigenvalues = A.eigenvals()
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# sp.pprint(eigenvalues)
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eigenvectors = A.eigenvects()
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# sp.pprint(eigenvectors)
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S, L = A.diagonalize()
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Labs = (L*L)**0.5
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plus = S*(L + Labs)*S.inv()/2
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minus = S*(L - Labs)*S.inv()/2
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Ahat = plus + minus
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plus.simplify()
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minus.simplify()
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print("Positive flux")
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r = sp.symbols("r")
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sp.pprint(plus.subs((kx*kx + ky*ky)**0.5, r))
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print("Negative flux")
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sp.pprint(minus.subs((kx*kx + ky*ky)**0.5, r))
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print("r = ")
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sp.pprint((kx*kx + ky*ky)**0.5)
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print("Evaluations:")
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print("plus (1, 0)")
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sp.pprint(plus.subs(kx, 1).subs(ky, 0))
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print("plus (0, 1)")
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sp.pprint(plus.subs(kx, 0).subs(ky, 1))
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print("plus (1/sqrt(2), 1/sqrt(2)")
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sp.pprint(plus.subs(kx, 1/2**0.5).subs(ky, 1/2**0.5))
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print("positive flux - negative flux")
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S = plus - minus
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S.simplify
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sp.pprint(S.subs((kx*kx + ky*ky)**0.5, r))
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