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Multifractal Methods for Anderson Transitions

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2020, Doctor of Philosophy, Ohio State University, Physics.
Two-dimensional Anderson Transitions have inspired study since the 1950s, but much about their critical properties remains unknown. I examine multifractality, the appearance of fractal dimensions which are not linearly related in the level sets of a probability density function, in the context of the wavefunction of a system undergoing an Anderson Transition. In Part II, I explore the multifractality of a system under strong magnetic field and its dependence on disorder on the underlying randomness in the placement of impurities in the sample. I relate this to field theoretic methods used to study matter fields existing on curved manifolds. In Part III, I explore the general problem of finding fields that are scale-invariant under the renormalization group in a broad set of Anderson Transitions described by non-linear sigma models. I use a method for decomposing the function spaces on these models' target spaces to find these entirely algebraically.
Ilya Gruzberg, PhD (Advisor)
Yuri Kovchegov, PhD (Committee Member)
Yuan-Ming Lu, PhD (Committee Member)
Thomas Lemberger, PhD (Committee Member)
254 p.

Recommended Citations

Citations

  • Charles, N. S. (2020). Multifractal Methods for Anderson Transitions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595519105865006

    APA Style (7th edition)

  • Charles, Noah. Multifractal Methods for Anderson Transitions. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1595519105865006.

    MLA Style (8th edition)

  • Charles, Noah. "Multifractal Methods for Anderson Transitions." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595519105865006

    Chicago Manual of Style (17th edition)