Researchers from the UCM and the Computational Simulation Center (CCS) have found a partial violation of the second law of thermodynamics in a quantum system known as the Hofstadter network, a violation that has no place in the framework of classical physics.
The Hofstadter network is a theoretical model with a square two-dimensional network through which quantum particles such as electrons or photons circulate. It has the peculiarity that when one of these particles completes a closed path in the network, it acquires a quantum phase.
This system models a class of two-dimensional materials (similar to graphene) with properties so exotic that they leave them outside the usual classification of conductors or insulators, responding to the name of topological insulators.
Among these properties, one of the most notable is that it presents currents at the edge, while the interior does not allow any conduction. In addition, these edge currents are extraordinarily robust in the presence of impurities in the material, which has put them in the crosshairs of scientific community for applications in spintronics, photonics and also in quantum computing.
In an article published in the journal Scientific Reports, the researchers Ángel Rivas and Miguel A. Martin-Delgado, from the Department of Theoretical Physics of the Complutense University and the CCS (Center for Computational Simulation), explain that they have studied the thermodynamic properties of this system placing it in the presence of two hot spots, one hot and one cold. For this they have formulated a quantum theory that describes this situation and solved the dynamic equations.
What the theoretical calculations predict is that heat transport behaves very far from what is expected from classical thermodynamics. Specifically, on one of the edges of the material a current is induced that flows from the cold focus to the hot focus, contrary to what is established by the second law of thermodynamics: it is not possible for the heat to flow spontaneously from a cold body to a body hotter
From the technological point of view, the second law of thermodynamics limits the energy efficiency achievable by devices such as motors, batteries, refrigerators, solar cells, etc.
However, when the rest of the edges and the interior of the material are taken into account, the result of the second law is recovered. This “partial” violation is an effect of this type of exotic quantum systems that has no place in the framework of classical physics.
In addition, these currents also have robustness against a type of impurities that meet certain patterns of symmetry related to the position of the thermal bulbs and the dissipative dynamics they induce.
This new phenomenon, called “protection by dissipative symmetries”, has never been observed and could give rise to new effects not only of fundamental interest, but of practical utility.
The work is part of a quantum simulation scenario, a discipline that seeks the study of these materials through devices of similar characteristics made with quantum control techniques, such as photonic networks and ultra-cold atoms.
These results encourage new and unexpected applications in the development of quantum technologies such as quantum simulators or quantum memories that present more robustness and operate under realistic conditions subject to thermal fluctuations.