Topology in many particle systems

In summary, the conversation is about someone seeking help in understanding lecture notes on geometry and topology in many-particle systems for a physics course at UC Berkeley. They mention having no background knowledge in topology and struggling with concepts such as the Hessian matrix. Another person responds, suggesting that the person may not have enough prerequisite knowledge for the course and that it may be difficult to explain everything on a message board. The original person expresses their interest in the notes and asks if there are more available. The other person provides a link to the professor's website where there are more notes available.
  • #1
tayyaba aftab
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  • #2
Interesting notes, but what exactly do you need help with? You have to be more specific.
 
  • #3
i basically have no bakground regarding topology that's why i cannot understand even from start:frown:like i don't know what hessian matrix is?
its diagnolization etc.
i started reading these notes many times but coudnt get any thing:cry:
what to do ?
 
  • #4
tayyaba aftab said:
i basically have no bakground regarding topology that's why i cannot understand even from start:frown:like i don't know what hessian matrix is?
its diagnolization etc.

Well, do you know what a http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant" is? This isn't topology, it's multi-variable calculus. It's the matrix of the partial derivatives of one set of coordinates with respect to another set of coordinates. (see link for examples)

A Hessian matrix is the same thing, just for the second-order derivatives.
 
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  • #5
:cry: buttttttttttttttttttttt what about rest of the notes?
:confused:
 
  • #6
Honestly, I think you're out of your league with those lecture notes. If you get stuck in the second paragraph of the first page on 'mathematical preliminaries' (things you should already know before taking that course), then you're simply not ready for it.

Specifically, multi-variable calculus (which covers Hessians) is first or second-year stuff for a physics undergrad, whereas those lecture notes are for a graduate course.

Nobody is going to even attempt to explain an entire course on a message board. And asking to fill in several years of missing prerequisite knowledge is just absurd.
 
  • #7
That said, I like these notes. Who wrote them? Are there more where these came from?
 
  • #8
genneth said:
That said, I like these notes. Who wrote them? Are there more where these came from?

I googled the info at the top of the notes - it's Joel Moore at UC Berkeley.

There are a few more on the Physics 250 site.
 
  • #9
Link:
http://socrates.berkeley.edu/~jemoore/Physics_250.html
 
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1. What is topology in many particle systems?

Topology is a branch of mathematics that studies the properties of shapes and spaces. In the context of many particle systems, topology refers to the arrangement and connectivity of particles in a given system.

2. How is topology relevant to many particle systems?

Topology plays a crucial role in understanding the behavior and properties of many particle systems. It helps to characterize the different phases and transitions of the system, as well as the emergence of collective behaviors and properties.

3. What are some examples of topological properties in many particle systems?

Examples of topological properties in many particle systems include the number of particles, the dimensionality of the system, the shape and geometry of the particles, and the connectivity between particles.

4. How does topology affect the dynamics of many particle systems?

The topological properties of a many particle system can greatly influence its dynamics. For example, the presence of topological defects or boundaries can lead to the emergence of novel behaviors and phase transitions.

5. How is topology in many particle systems studied?

Topology in many particle systems is studied using a combination of theoretical and computational methods. This includes tools from topology, statistical mechanics, and computer simulations to analyze and understand the behavior of complex systems.

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