Regarding Drude theory and AC conductivity of metal

In summary, the conversation discusses representing fields in complex notations for convenience and the need for the imaginary part of the field to satisfy an equation, even though it is designated by ourselves. It also mentions combining two real functions into two complex functions and using a complex phase factor to recover the original functions.
  • #1
otaKu
27
2
IMG_20160622_122232_HDR_1466578387182.jpg

This snapshot is from the book Solid State Physics by Ashcroft,Mermin. They represented the Field and Momentum as the real part of a complex function. As far as what I understand, we represent fields in complex notations for our own convenience over the standard real representation which results in computational complexities. Why then does the imaginary part of the field which we have designated by ourselves need to satisfy the equation 1.24 which the real part of the field(the actual field) satisfies?
 
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  • #2
You combine two real functions into two complex functions, the second one being the adjoint function of the first.E.g you can combine cos x and sin x into exp ix and exp -ix. Hence both the real and the imaginary part of the complex function are solutions of the equation you want to solve. Whether you recover the cos or sin function taking the real part, you can decide by multiplying the complex function with a complex phase factor.
 
  • #3
Thanks for the input! It was helpful.
 

FAQ: Regarding Drude theory and AC conductivity of metal

What is Drude theory and how does it explain AC conductivity of metals?

Drude theory is a classical model that explains the behavior of electrons in a metal. It assumes that electrons are free to move in a metal and that they are scattered by the metal ions. When an alternating electric field is applied to a metal, the electrons will experience a force and will move in response, leading to the flow of current. This theory also explains the relationship between the frequency of the alternating field and the conductivity of the metal.

What is the role of temperature in Drude theory and AC conductivity of metals?

Temperature plays a crucial role in Drude theory as it affects the movement of electrons and the scattering process. As temperature increases, the ions in the metal vibrate more vigorously, causing more frequent collisions with the electrons. This increases the resistance of the metal, leading to a decrease in conductivity. In contrast, at lower temperatures, the ions vibrate less, resulting in fewer collisions and higher conductivity.

Can Drude theory be applied to all types of metals?

No, Drude theory is only applicable to metals with a high density of free electrons, such as copper, silver, and gold. It cannot be applied to insulators or semiconductors, where the behavior of electrons is significantly different.

How does the skin effect relate to Drude theory and AC conductivity of metals?

The skin effect is a phenomenon where the AC current tends to flow near the surface of a metal conductor instead of uniformly throughout its cross-section. This is due to the repulsion between the electrons and the ions in the metal, as predicted by Drude theory. As the frequency of the AC current increases, the skin depth decreases, resulting in a higher resistance and lower conductivity of the metal.

Is Drude theory still relevant in modern physics?

While Drude theory is a simplified model, it still provides a good understanding of the behavior of electrons in metals. However, it does not take into account quantum effects, which are essential in modern physics. Therefore, it is often used as a starting point for more advanced theories and calculations of AC conductivity in metals.

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