Relaxation time = displacement lifetime of fermi sphere?

In summary, the conversation is about the confusion regarding the relationship between relaxation time and the lifetime of fermi sphere displacement in the presence of an electric field. The equations for electrical conductivity and resistivity are also mentioned, and the question of how to calculate resistivity for copper is asked.
  • #1
neu
230
3

Homework Statement



I just want to clear this up, I am a little confused:

when an electric field is applied there is a force on the electron K-states thus displacing the fermi surface/sphere

Is the relaxation time ([tex] \tau[/tex])= lifetime of fermi sphere displacement

or is lifetime of displacement= reciprocal relaxation time

both are labebel as [tex]\tau[/tex] in my notes and related as below but how can they be the same?


Homework Equations



[tex] \sigma = \frac{n e^2 \tau}{m}[/tex] electrical conductivity

[tex] \rho = \frac{1}{\sigma}=\frac{m}{n e^2 \tau}[/tex] electrical resistivity
 
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  • #2
Given the following data on copper, how do i calculate the resistivity?

Relaxation time: 2.50e10-14s
Density: 8940Kgm-3
molar mass: 63.5g

is there an equation for it.
 

1. What is the significance of relaxation time in a fermi sphere?

The relaxation time in a fermi sphere refers to the average time it takes for an excited particle to return to its original state. This is an important concept in understanding the behavior of particles in a fermi sphere, as it determines the rate of energy dissipation and the overall stability of the system.

2. How is the relaxation time related to the displacement lifetime?

The relaxation time and displacement lifetime are essentially the same concept, with the only difference being the units in which they are measured. The relaxation time is typically measured in seconds, while the displacement lifetime is measured in distance (such as meters or angstroms).

3. What factors affect the relaxation time in a fermi sphere?

The relaxation time in a fermi sphere is influenced by several factors, including the density of states, the scattering mechanisms, and the temperature of the system. Additionally, the type of material and its properties can also impact the relaxation time.

4. How does the relaxation time change with temperature in a fermi sphere?

The relaxation time in a fermi sphere is inversely proportional to the temperature of the system. This means that as the temperature increases, the relaxation time decreases, and particles are able to dissipate their energy more quickly.

5. What are some real-world applications of understanding relaxation time in a fermi sphere?

Understanding relaxation time in a fermi sphere is crucial in various fields of science, including materials science, condensed matter physics, and semiconductor technology. It is also relevant in fields such as electronics and optoelectronics, as it helps in the design and optimization of devices such as transistors and solar cells.

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