Relation between Polarization and electric field for instantaneous response

In summary, the conversation discusses the time independence of susceptibility and its relation to an equation in the frequency domain. The Kramers-Kronig relation and Noll's restrictions are mentioned as well as the standard procedure of Fourier or Laplace transforming the equation.
  • #1
Algarion
1
0
Dear all

In case of a material that instantaneous responds to an external applied field is

P(r,t)=χE(t)

Is the suseptibility then time independent? And if so, how it is possible to derive from the above equation an equation in the frequency domain?

Yours
 
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  • #2
The most simple relation (the Kramers-Kronig relation) is found by only demanding the susceptibility be causal- P(t) can only depend on E(t'), where t' < t (extend the results to a lightcone for spatially-varying E).

The general restrictions on the susceptibility (or any constitutive relation) were laid down by Noll in the '60s, and are fairly general. AFAIK, there is no requirement that the susceptibility *may not* be time-dependent. This is covered in several books, including the Encyclopedia of Physics (Vol III, Non-linear field theories).

For the frequency domain, the usual procedure is to Fourier transform (or Laplace transform) the equation.
 

What is polarization?

Polarization is the process of separating positive and negative charges within an object, resulting in an electric dipole moment.

How is polarization related to electric field?

Polarization occurs in response to an external electric field. The strength and direction of the electric field determine the amount and orientation of polarization that will occur.

What is the difference between instantaneous and permanent polarization?

Instantaneous polarization occurs when an electric field is applied to a material, causing the electrons to shift momentarily. Permanent polarization, on the other hand, occurs when a material retains its polarization even after the electric field is removed.

How does the electric field affect the strength of polarization?

The strength of polarization is directly proportional to the strength of the electric field. As the electric field increases, the polarization of the material also increases.

Can polarization occur in non-conductive materials?

Yes, polarization can occur in non-conductive materials. This is because non-conductive materials still have electrons that can be shifted in response to an electric field.

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