root / ase / transport / greenfunction.py @ 1
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| 1 | 1 | tkerber | import numpy as np |
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| 2 | 1 | tkerber | |
| 3 | 1 | tkerber | class GreenFunction: |
| 4 | 1 | tkerber | """Equilibrium retarded Green function."""
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| 5 | 1 | tkerber | |
| 6 | 1 | tkerber | def __init__(self, H, S=None, selfenergies=[], eta=1e-4): |
| 7 | 1 | tkerber | self.H = H
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| 8 | 1 | tkerber | self.S = S
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| 9 | 1 | tkerber | self.selfenergies = selfenergies
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| 10 | 1 | tkerber | self.eta = eta
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| 11 | 1 | tkerber | self.energy = None |
| 12 | 1 | tkerber | self.Ginv = np.empty(H.shape, complex) |
| 13 | 1 | tkerber | |
| 14 | 1 | tkerber | def retarded(self, energy, inverse=False): |
| 15 | 1 | tkerber | """Get retarded Green function at specified energy.
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| 16 | 1 | tkerber |
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| 17 | 1 | tkerber | If 'inverse' is True, the inverse Green function is returned (faster).
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| 18 | 1 | tkerber | """
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| 19 | 1 | tkerber | if energy != self.energy: |
| 20 | 1 | tkerber | self.energy = energy
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| 21 | 1 | tkerber | z = energy + self.eta * 1.j |
| 22 | 1 | tkerber | |
| 23 | 1 | tkerber | if self.S is None: |
| 24 | 1 | tkerber | self.Ginv[:] = 0.0 |
| 25 | 1 | tkerber | self.Ginv.flat[:: len(self.S) + 1] = z |
| 26 | 1 | tkerber | else:
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| 27 | 1 | tkerber | self.Ginv[:] = z
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| 28 | 1 | tkerber | self.Ginv *= self.S |
| 29 | 1 | tkerber | self.Ginv -= self.H |
| 30 | 1 | tkerber | |
| 31 | 1 | tkerber | for selfenergy in self.selfenergies: |
| 32 | 1 | tkerber | self.Ginv -= selfenergy.retarded(energy)
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| 33 | 1 | tkerber | |
| 34 | 1 | tkerber | if inverse:
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| 35 | 1 | tkerber | return self.Ginv |
| 36 | 1 | tkerber | else:
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| 37 | 1 | tkerber | return np.linalg.inv(self.Ginv) |
| 38 | 1 | tkerber | |
| 39 | 1 | tkerber | def calculate(self, energy, sigma): |
| 40 | 1 | tkerber | """XXX is this really needed"""
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| 41 | 1 | tkerber | ginv = energy * self.S - self.H - sigma |
| 42 | 1 | tkerber | return np.linalg.inv(ginv)
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| 43 | 1 | tkerber | |
| 44 | 1 | tkerber | def apply_retarded(self, energy, X): |
| 45 | 1 | tkerber | """Apply retarded Green function to X.
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| 46 | 1 | tkerber |
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| 47 | 1 | tkerber | Returns the matrix product G^r(e) . X
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| 48 | 1 | tkerber | """
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| 49 | 1 | tkerber | return np.linalg.solve(self.retarded(energy, inverse=True), X) |
| 50 | 1 | tkerber | |
| 51 | 1 | tkerber | def dos(self, energy): |
| 52 | 1 | tkerber | """Total density of states -1/pi Im(Tr(GS))"""
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| 53 | 1 | tkerber | if self.S is None: |
| 54 | 1 | tkerber | return -self(energy).imag.trace() / np.pi |
| 55 | 1 | tkerber | else:
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| 56 | 1 | tkerber | GS = self.apply_retarded(energy, self.S) |
| 57 | 1 | tkerber | return -GS.imag.trace() / np.pi
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| 58 | 1 | tkerber | |
| 59 | 1 | tkerber | def pdos(self, energy): |
| 60 | 1 | tkerber | """Projected density of states -1/pi Im(SGS/S)"""
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| 61 | 1 | tkerber | if self.S is None: |
| 62 | 1 | tkerber | return -self.retarded(energy).imag.diagonal() / np.pi |
| 63 | 1 | tkerber | else:
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| 64 | 1 | tkerber | S = self.S
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| 65 | 1 | tkerber | SGS = np.dot(S, self.apply_retarded(energy, S))
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| 66 | 1 | tkerber | return -(SGS.diagonal() / S.diagonal()).imag / np.pi |