Kubo formula for thermopower (Seebeck coefficient)

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SUMMARY

The Kubo formula for thermopower, defined as S = L_{21}/L_{11}, relates electric conductivity (L_{11}) to real-time current-current correlations. The discussion emphasizes the need to express heat conductivity in terms of heat current correlations to derive L_{21}. A critical question raised is whether the gradient of 1/T can be treated as an external force in this context. References to Landau Lifshitz suggest that established theoretical frameworks may provide insights into this relationship.

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  • Understanding of Kubo formula in statistical mechanics
  • Familiarity with electric and heat conductivity concepts
  • Knowledge of real-time current-current correlations
  • Basic principles of thermoelectric effects and Seebeck coefficient
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  • Research the derivation of the Kubo formula for thermopower
  • Study the relationship between heat current and electric current correlations
  • Examine the role of temperature gradients in thermoelectric phenomena
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Physicists, materials scientists, and researchers in thermoelectric materials seeking to deepen their understanding of thermopower and its theoretical foundations.

lyuchn
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I have a long-standing puzzle about the Kubo formula of thermopower S=L_{21}/L_{11}.

The electric conductivity (L_{11}) can be expressed in terms of real time current-current correlations.
Similarly, the heat conductivity can be expressed in terms of real time correlations
of heat currents.

So how to relate thermopower, which measures the electric current driven by a temperature gradient, to some kind of current-current correlation. Here it should be the correlation between heat current and electric current. But how to derive this formula for L_{21}?
Can we simply take the gradient of 1/T as an external force? Why this holds?
 
Did you have a look at Landau Lifshitz? Would be my best guess to find something.
 

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