# Louella Vasquez

#### Mulrifractional Electron State

### How is the work you are currently doing relevant to everyday life?

The numerical methods and analyses developed in this work can be well applied to any multifractal distributions such as land slide dynamics, stock market time series and heartbeat dynamics. This is useful to understand more about the true nature of these complex distributions.

### What does your research hope to achieve?

Our work has shown that just by studying the fluctuations or the multifractal characteristics of the electron state at the disorder-induced metal to insulator transition, it is now possible to determine the physical properties of the critical transition without resorting to the usual complicated numerical methods or performing transport measurements. This work has used more than 2.5 million samples amounting to more than 2 Terabytes of data, using very large system sizes which are unprecedented in this field. Important results of this work have been published in two papers, both in Physical Review Letters which is considered as the best pure physics journal.

### What does the image show?

This is a picture of a multifractal electron wave in a strongly disordered cubic environment. The electron state shown here is neither a metal (uniform-sized boxes all around in the cube) nor an insulator (isolated large boxes) but contains characteristics of both. The bigger the box size is the greater is the chance of finding an electron at that site. This complex structure persists even if we enlarge or reduce the cube. Hence we say that the electron is a multifractal.