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redrum419_7
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I am a Physics major/ Math minor and would like to know what sort of undergrad upper-level math classes would be the most useful for Condensed Matter or Materials Science Theory?
Physics Monkey said:On the more theoretical side you might try looking for classes in combinatorics, algorithms, complexity (classical). In my experience it helps to speak some of these languages in the theoretical quantum computing field. Advanced linear algebra e.g. numerical methods, abstract vector spaces, etc. is certainly fundamental to quantum computing research.
If you're more interested in physical realizations of quantum computers then the picture is different. Some familiarity with the above subjects may be helpful, but one will have to work a lot more closely with experiments (for which advanced mathematical training is often less helpful).
If you provide more information about your interests, then we can probably get a better idea of what might be a good fit for you mathwise.
I definitely want the math minor though so would topology or differential geometry help? I know they play some role in QFT.
QFT in the high energy QFT's people sense is not used in condensed matter. There is condensed matter quantum field theory, but it deals with entirely different problems and approaches to dealing with them than the high-energy QFT stuff. Knowing high-energy QFT is unlikely to help you with the condensed-matter theory.redrum419_7 said:Does QFT play a role in quantum computer research? I definitely want the math minor though so would topology or differential geometry help? I know they play some role in QFT.
It does have to do something with many-body physics. Many modern many-body approaches aimed for model problems in condensed matter argue in terms of information theory (say, density matrix renormalization grop, tensor networks, multiscale entanglement renormalization, general fermionic circuits). If you study many-body methods (which are at the heart of many branches of condendes matter theory), there is a good chance you'll come across things like area laws and all kinds of strange information entropies.chill_factor said:quantum information theory seems to have very little to do with materials science.
About topology: While topology does play a role in these branches of physics (particularly in 2D systems), the level and type of topology is again very different from what mathematicans study as "topology". You will never encounter a "topological space" without any superstructure or any of the associated theorems anywhere in physics. And even if your topology class is about what one would more likely associate with the word "topology" (tori, holes, etc), there is no need to study it from a mathematical perspective if you are willing to simply believe a few intuitive fundamental theorems instead of spending one or two years working towards their proofs.
chill_factor said:quantum information theory seems to have very little to do with materials science.
what level of math is needed to even take a graduate level condensed matter physics class for physicists, never mind go into theory?
Math is essential in condensed matter and materials science theory as it provides the necessary tools for understanding and predicting the behavior of materials at the atomic and molecular level. It allows scientists to develop models and equations that describe the complex interactions between atoms and molecules, which are crucial for designing new materials and improving existing ones.
Some common mathematical concepts used in condensed matter and materials science theory include differential and integral calculus, linear algebra, differential equations, and statistical mechanics. These concepts are used to describe and analyze the properties and behavior of materials at the atomic and molecular level.
By using mathematical models and equations, scientists can predict the properties of materials based on their atomic and molecular structure. For example, the band theory of solids uses mathematical concepts to predict the electronic properties of materials, such as their conductivity and optical properties.
Yes, math plays a crucial role in the design of new materials. By using mathematical models and simulations, scientists can predict how different materials will behave under certain conditions and make informed decisions about which materials to use for specific applications. Mathematical optimization techniques are also used to design new materials with desired properties.
Yes, there are several mathematical challenges in condensed matter and materials science theory. One of the main challenges is developing accurate and efficient mathematical models to describe the behavior of complex materials. Another challenge is incorporating quantum mechanics into mathematical models to accurately predict the behavior of materials at the atomic scale.