The boltzmann transport equation double integral

In summary, The scattering term in the Boltzmann transport equation involves a double integral, with each case integrating over different variables. This is necessary in order to account for the various scattering processes that can occur in a system. This information can be found in the article referenced, as well as in Landau & Lifschitz's work on Kinetic Theory. It is also important to pay attention to other parts of the equation in order to fully understand its implications. Any additional help or resources would be greatly appreciated.
  • #1
shaun evans
1
0
hi,

i've never posted on here before but would appreciate any help given for this question.

The scattering term (4th term) in the Boltzmann transport equation contains a double integral.

What are you integrating over in each case and why is this?

this may be a simple question but as i said any help would be gratefully appreciated.

thanks,

shaun
 
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  • #2
I don't have access to this article, if you do, then I hope it proves a valuable source of information.
http://adsabs.harvard.edu/abs/1960AmJPh..28...1D

Other than that, I vaguely remember that the transport equation was dealt with by Landau & Lifschitz in the volume on Kinetical theory.

Also, you may want to check this part, too.
 

1. What is the Boltzmann transport equation double integral?

The Boltzmann transport equation double integral is a mathematical equation used to describe the behavior of particles in a system, such as electrons in a semiconductor material. It takes into account the interactions between particles and their environment, and allows us to predict their movement and distribution over time.

2. How is the Boltzmann transport equation double integral derived?

The Boltzmann transport equation double integral is derived from the Boltzmann transport equation, which is a more general form of the equation. The double integral specifically takes into account the scattering processes that occur between particles, such as collisions with impurities or phonons.

3. What are the assumptions made in the Boltzmann transport equation double integral?

The Boltzmann transport equation double integral makes several assumptions, such as the particles being in thermal equilibrium, the system being in a steady-state, and the particles following a Maxwell-Boltzmann distribution. These assumptions allow for a simplified model of the system, but may not accurately describe real-world scenarios.

4. What are the main applications of the Boltzmann transport equation double integral?

The Boltzmann transport equation double integral is commonly used in the field of semiconductor physics, where it helps to model the behavior of electrons in materials. It is also used in other areas of physics, such as plasma physics, to study the behavior of particles in high-energy environments.

5. What are the limitations of the Boltzmann transport equation double integral?

While the Boltzmann transport equation double integral is a useful tool for studying particle behavior in certain systems, it has its limitations. It assumes that particles only interact through binary collisions, which may not be the case in more complex systems. It also does not take into account quantum effects, which may be important in certain scenarios.

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