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Mathematical Physics : School of Mathematics and Statistics
Kaiser, Physical Review A 69 , Upadhyaya, J. Rieu, J. Glazier and Y. Yee, P. Kosteniuk, G. Chandler, C. Biltoft and J. Bowers, Boundary-Layer Meteorology 66 , Mendes, L. Malacarne and E. The theory of linear bounded and unbounded operators is developed, focusing on results needed for the theory of Schr"dinger operators. The spectral theory for self-adjoint operators is given in some detail. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines. Skip to main content Skip to table of contents.
Advertisement Hide. Front Matter Pages i-xxiii. Front Matter Pages Pages Spaces of Test Functions. Schwartz Distributions. Calculus for Distributions. Distributions as Derivatives of Functions. Tensor Products. Convolution Products. Applications of Convolution. Upon variation of these parameters the system exhibits different physical phases with qualitatively different features. Some of these phases can be distinguished by a discrete invariant that takes one value in one phase and another one in a second.
This observation provides a link to the mathematical field of topology which studies the properties of geometric objects, such as knots, up to continuous deformations.
Communications in Mathematical Physics
In view of this connection, one frequently speaks about topological phases of matter. There are various prominent examples which have only been discovered in the last couple of years - first theoretically, then also experimentally. Building on the example of Kitaev's so-called Majorana chain, a simple free fermion model of a 1D superconductor, the Vacation Scholar will develop some intuition about the associated topological invariant which, essentially, counts the number of Majorana edge modes. She or he will then apply these insights to a closely related system of so-called parafermions and try to derive a topological invariant for these.
Contact: Thomas Quella Thomas.