# Superconductivity model of 100,000 equations now contains only 4 thanks to AI

(ORDO NEWS) — The electrons zipping through the grid don’t behave at all like pretty silver balls in a pinball machine.

They twist and turn in a collective dance, following the quirks of an undulating reality that is hard enough to imagine, let alone calculate.

And yet, scientists have managed to do just that by capturing the movement of moving electrons. about the square lattice in simulations that have so far required hundreds of thousands of separate equations.

Using artificial intelligence (AI) to reduce this problem to four equations, physicists have done their job. studying the emerging properties of complex quantum materials has become much easier.

In doing so, this computational feat could help solve one of the most difficult problems in quantum physics, the “many electrons” problem, which attempts to describe systems containing a large number of interacting electrons.

It could also advance the truly legendary tool for predicting the behavior of electrons in solid materials, the Hubbard model, improving our understanding of how convenient phases are of matter such as superconductivity.

Superconductivity is a strange phenomenon that occurs when a stream of electrons flows unhindered through a material, losing little or no energy as it travels from one point to another.

Unfortunately, most of the practical means of creating such a state are based on insanely low temperatures, if not ridiculously high pressures.

The use of superconductivity at temperatures close to room temperature could lead to much more efficient electrical networks and devices.

Because achieving superconductivity under more reasonable conditions remains a noble goal, physicists have begun using models to predict how electrons might behave under different conditions. circumstances, and therefore what materials make suitable conductors or insulators.

These models have their work for them. After all, electrons don’t roll around a network of atoms like tiny balls, with well-defined positions and trajectories.

Their activity is a mess of probability, influenced not only by their environment, but also by the history of their interactions with other electrons they encounter along the way.

When electrons interact, their fates can be closely intertwined, or “entangled”. Modeling the behavior of a single electron means simultaneously tracking the range of possibilities of all electrons in the model system, which exponentially complicates the computational problem.

The Hubbard model is a decades-old mathematical model that describes quite accurately by confusing the movement of electrons through a lattice of atoms.

Over the years, much to the delight of physicists, a deceptively simple model has been experimentally implemented in the behavior of a wide range of complex materials.

With ever-increasing computing power, researchers have developed numerical models based on the Hubbard Physical Model that allows them to understand the role of the underlying lattice topology.

For example, in 2019, researchers proved that the Hubble model is capable of representing superconductivity higher than superhigh. low temperatures, giving researchers the green light to use the model to better understand the area.

This new study could be another big leap, greatly simplifying the number of equations needed. Researchers have developed a machine learning algorithm to improve on a mathematical tool called a renormalization group, which physicists use to study changes in a material system when properties such as temperature change.

“Essentially, it’s a machine that has the ability to detect hidden patterns,” says physicist and lead author Domenico Di Sante of the University of Bologna in Italy of the team’s program.

“We start with this huge object, which is made up of all these connected… together differential equations,” each representing pairs of entangled electrons, “then we use machine learning to turn it into something so small that it can be counted on fingers.” ,” Di Sante says of their approach.

The researchers demonstrated that their data-driven algorithm can efficiently learn and replicate the dynamics of the Hubbard model using just a few equations four to be precise and without sacrificing accuracy.

“When we saw the result, we said: “Wow, this is more than we expected.” We really managed to capture the relevant physics,” says Di Sante.

It took weeks to train the machine learning program with the data, but Di Sante and colleagues say it can now be adapted to work with other, tantalizingly compressed data. matter problems.

The simulation so far has only covered a relatively small number of variables in the lattice network, but the researchers expect their method to be scalable enough to other systems.

If so, it could be used in the future to test the suitability of conductive materials for applications involving clean energy generation, or to help develop materials that could one day achieve this elusive room-temperature superconductivity.

At the moment, the work demonstrates the possibility of using AI. to extract compact representations of dynamical electrons, “a goal of paramount importance for the success of advanced quantum field theory methods to solve the many-electron problem,” the researchers conclude in their summary.

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