How to understand diffusive and ballistic transport?

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Discussion Overview

The discussion centers around the concepts of diffusive and ballistic transport, exploring their definitions, characteristics, and implications in various contexts such as gases and electronic systems. Participants seek to clarify their understanding of these transport mechanisms and their mathematical formulations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that diffusive transport involves particles moving from high to low density regions and is characterized by the equation ##\langle x^2(t) \rangle = Dt##, indicating a random walk behavior.
  • Another participant notes that "ballistic" transport refers to scenarios where the scattering length is comparable to or larger than the device size, implying less frequent scattering compared to diffusive transport.
  • There is a mention of the "drunk student in a forest" analogy to illustrate diffusive transport, where a particle is repeatedly scattered, contrasting with the linear nature of ballistic transport.
  • A participant expresses confusion regarding the relationship between ballistic transport and kinetic energy, questioning how energy behaves in diffusive transport.
  • One participant provides a link to a resource related to random walk diffusion, suggesting it may help clarify the concepts discussed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and implications of diffusive and ballistic transport, with multiple competing views and some uncertainty regarding the relationship between transport mechanisms and energy.

Contextual Notes

Participants highlight the need for context in discussing transport mechanisms, such as whether the focus is on gases or electronic systems. There is also a reliance on analogies and examples that may not be universally understood.

KFC
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Hi there,
I am always confusing in the difference between diffusive and ballistic transport. My understanding on the diffusive transport is from it's name, particles diffuse from the high density region into the low density region. I think the diffusion happens towards all direction, is it why usually it is formulated as ##\langle x^2(t) \rangle = Dt## ? For the ballistic transport, it is very confusing where is the term ballistic from. But my understanding is the transport is linear, is that correct?

I saw that in some article, there mentions transport in momentum. It looks like that the ballistic transport corresponding to quadratic growth of kinetic energy. I don't understand why but if that's the case, how does it look like for energy for diffusive transport in momentum?
 
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I think you need to put your question into some sort of context. Are you talking about transport in gases? Or say electrons in a 2DEG?

Regardless, "ballistic" usually means that the scattering length (the mean length a particle travels before being scattered) is of the same order of magnitude or larger than the device size (i.e. the space/surface it travels in/on). Diffuse transport means that the particle is being repeatedly scattered (see the "drunk student in a forest" problem in statistical physics).
 
f95toli said:
(see the "drunk student in a forest" problem in statistical physics).
Why not give a link instead of search terms that lead nowhere (into a dark forest :smile: )
 
BvU said:
Why not give a link instead of search terms that lead nowhere (into a dark forest :smile: )

I don't have a link. However, it is a problem I've seen in several books. It is just "fun" version of the normal derivation of the random walk derivation of a diffusion equation, instead of a particle bouncing around in a graphyou imagine a very drunk student trying to find his/her way out of a circular forest. The "rules" are that the student will walk in a straight line until he/she walks into a tree and falls over, he/she will then get up and walk in a new random direction.
The goal of the exercise is to figure how far the student will have traveled after some time t (and when he/she will emerge from the forest).

Edit: A Google search for "random walk diffusion drunk" gives e.g. the following hit
http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L13/Lecture13.pdf
 
Thanks for reference. It looks like a very good article to read.

When I first think of the problem, I am thinking of the transport in gas.
 

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