The Schrodinger equation rules quantum physics. It deals with and describes the universe at the scale of atoms. The equation, which describes in its simplest form, is given by
Where H is the Hamiltonian of the system and E is the energy eigenvalue, and ψ is the wavefunction describing the system. The Hamiltonian H is given by
It gives energy to the system.
The equation becomes much more complicated for systems with many particles and interactions. As the number of particles in the system increases, the number of equations increases. Many times (well, most of the times), the Schrodinger equation is not solvable for just a one-particle system, let alone a many-body system. It’s due to the partial differential equations, which are generally not solvable analytically.
Now, Physicists have used deep learning to reduce a 100,000 equations problem to just four equations without any accuracy loss. The problem was analyzing how an electron behaves as it moves in a grid-like lattice. Interaction happens when two or more electrons are present at the same lattice location. Scientists can study how electron behavior leads to desired phases of matter. Additionally, the model is a providing ground for novel techniques before they are applied to complex quantum systems.
The problem demands a significant amount of computer power, even for a small number of electrons, using state-of-the-art computational techniques. Physicists have to deal with all of the electrons at once rather than one at a time because when electrons interact, their destinies can become quantum mechanically entangled. This means that even though they are far away on distinct lattice sites, the two electrons cannot be dealt with separately. Since there are more entanglements with more electrons, the computing challenge becomes exponentially more difficult. Renormalization groups are a tool that can be used to examine a quantum system. The Hubbard model is one example of a system in which physicists use this mathematical tool to examine how the behavior of a system varies as we alter properties like temperature or consider the properties on various scales. Unfortunately, there may even be millions of individual equations in a renormalization group that must be solved to maintain track of all couplings between electrons without making any sacrifices. The equations themselves are challenging since each depicts two electrons’ interactions.
This approach can potentially solve much more complex problems.
This Article is written as a research summary article by Marktechpost Staff based on the research paper 'Deep Learning the Functional Renormalization Group'. All Credit For This Research Goes To Researchers on This Project. Check out the paper and reference article. Please Don't Forget To Join Our ML Subreddit
Asif Razzaq is an AI Journalist and Cofounder of Marktechpost, LLC. He is a visionary, entrepreneur and engineer who aspires to use the power of Artificial Intelligence for good.
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Asif was featured by Onalytica in it’s ‘Who’s Who in AI? (Influential Voices & Brands)’ as one of the ‘Influential Journalists in AI’ (https://onalytica.com/wp-content/uploads/2021/09/Whos-Who-In-AI.pdf). His interview with him was also featured by Onalytica (https://onalytica.com/blog/posts/interview-with-asif-razzaq/).