Theoretical physicists Yoshimichi Teratani and Akira Oguri of Osaka City University and Rui Sakano of Tokyo University have developed mathematical formulas that describe a physical phenomenon that occurs in quantum dots and other deposited materials. Formulas published in a journal *Letters of physical examination*, could be applied to further theoretical research on the physics of quantum dots, ultracold atomic gases and quarks.

It’s a “condo effect.” This effect was first described in 1964 by Japanese theoretical physicist Yun Kondo in some magnetic materials, but it seems to be happening now in many other systems, including quantum dots and other nanoscale materials.

Typically, the electrical resistance in metals decreases as the temperature drops. But in metals containing magnetic impurities, this only happens up to the critical temperature, over which the resistance increases with decreasing temperature.

Scientists have finally been able to show that at very low temperatures close to absolute zero, electronic spins become entangled with magnetic impurities, forming a cloud that shows their magnetism. The shape of the clouds changes with further drops in temperature, leading to an increase in resistance. The same effect occurs when other external “perturbations” are applied to the metal, such as voltage or a magnetic field.

Teratani, Sakano and Oguri wanted to develop mathematical formulas to describe the evolution of this cloud in quantum dots and other nanoscale materials, which is not an easy task.

To describe such a complex quantum system, they started with an absolute zero system where a well-established theoretical model, namely Fermi’s fluid theory, is applicable to electron interaction. They then added a ‘correction’ describing another aspect of the system against external disturbances. Using this technique, they wrote formulas that describe electric current and its oscillation through quantum dots.

Their formulas indicate that electrons interact within these systems in two different ways that contribute to the condo effect. First, the two electrons collide with each other, creating well-defined quasiparticles that propagate within condo clouds. More importantly, there is an interaction called the contribution of the three bodies. This is when two electrons combine in the presence of a third electron, causing an energy shift of the quasiparticles.

“Predictions of formulas could soon be investigated experimentally,” says Oguri. “Studies similar to this research have just begun,” he adds.

The formulas could also be extended to understand other quantum phenomena, such as the motion of quantum particles through quantum dots associated with superconductors. Quantum dots can be the key to the realization of quantum information technologies, such as quantum computers and quantum communication.

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