This thesis studies quantum mechanics on fractals, which are structures similar on different scales. Fractals can be found everywhere in nature, from snowflakes and clouds to the shapes of rivers and flowers. But one can also take a look at more peculiar objects. By recent experiments, it was demonstrated that quantum fractals can be build. Therefore we studied their theory.
We have found that physical properties of a quantum fractal can be different from those in usual materials. However, these properties depends on fractal geometry. Some fractals are like crystals, some behave as random systems, and others are described by completely new physics. This physics could be useful not only for new electronic technologies, but it is also interesting in connection with deep theories about quantum world.
Askar Iliasov was born on 27th of July in Ufa, Soviet Union. In 2009, Askar started to study physics in Moscow Institute of Physics and Technology. After obtaining Master of Science degree in 2015, he worked a few years as a researcher in Institute of Space Research, Russian Academy of Science. In 2017 he started his PhD research under the supervision of prof. dr. Mikhail Katsnelson and prof. dr. Shengjun Yuan. Askar currently works as a postdoc at the Theory of Condensed Matter department of the Radboud University.