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JYU Condensed Matter Theory
usadelndsoc
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eff47c46
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eff47c46
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2 years ago
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patavirt
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# Gauge-invariant discretization
We do the discretization of the Usadel equation as follows. We first
discretize the action $
`S`
$, and derive the discrete saddle-point
equation from the discretized action. This simplifies things somewhat,
because proper handling of the gauge fields is simpler to do
in the action formulation.
discretize the action $
`S`
$. The discrete saddle-point equation or expressions
for currents are not derived analytically, but instead obtained from the computer
implementation of the action via automatic differentiation (AD).
This simplifies things somewhat, because proper handling of the gauge fields is
simpler to do in the action formulation.
The action is
```
math
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