Juan Jose Mendoza Arenas

From processes we find in our daily life, to effects in nanoscale devices, interactions between different constituent elements of a system are of vital importance. Several prominent cases take place in quantum materials, where many-body correlations are responsible for spectacular collective phenomena such as magnetism and superconductivity. A huge effort has been made for several decades to understand the nature and consequences of these correlations in diverse systems. However, many questions remain to be solved. For example, the mechanism underlying high-Tc superconductivity has not been clarified, or the extent to which quantum heat-to-work conversion devices truly outperform classical machines is yet to be firmly established. The field of correlated many-particle systems is full of exciting and wide-open problems, whose solution would provide society with new clean and efficient technologies. A key property of quantum materials is their high sensitivity to external stimuli, which manifests in their wide variety of electric, magnetic, optical, mechanical and thermal responses. Because of this, they are very promising for implementing and selectively controlling diverse phases for technological applications. In recent years, seminal advances have led to the development of control strategies whose potential lies in driving quantum matter to far-from-equilibrium states, which have the potential to feature effects absent or more robust than those in (close to) equilibrium setups. My computational research aims at unravelling the physics of such nonequilibrium states, determine the conditions under which they optimally perform certain processes, and establish scenarios in which they can be implemented. For this I consider two mechanisms of out-of-equilibrium driving, namely boundary driving by unequal leads and excitation by light in cavities, corresponding to different paths for implementing cutting-edge technologies. A nice recent example of this line of research is found here: <a href="https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.010341" data-uw-rm-brl="PR" data-uw-original-href="https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.010341">PRX QUANTUM: Giant Rectification in Strongly Interacting Driven Tilted Systems</a> To analyze the physics of these scenarios, my research mostly relies on specialized numerical simulations based on tensor network theory. The latter constitutes the most powerful family of algorithms for the study of strongly-correlated quantum systems. Its vast success, however, has made it a key methodology in many other areas of science. A remarkable recent example corresponds to the computation of classical fluid turbulence, being more efficient than direct numerical simulations. Some of my future research will apply and enhance this approach to study turbulence for technological problems.