Recently applications of the Chern number have attracted a lot of interest. The notable example is the quantum Hall effect. It can be argued that the precise quantization of Hall conductance should be related to topological nature of the systems. In fact the quantization of the Hall conductance in two-dimensional periodic potentials was proved by using the Kubo formula by Thouless, Kohmoto, Nig...

We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity particle density ratio, which is analogous the entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds filling fraction characterizes quantum states, and hence it could be discussed Haldane's zero-field system. also consider dissipationless ...

In this paper, we highlight two q-series identities arising from the “five guidelines” approach to enumerating lecture hall partitions and give direct, qseries proofs. This requires two new finite corollaries of a q-analog of Gauss’s second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained com...

Rabindra R. Bajracharya and John R. Thompson Department of Physics, 301 Weniger Hall, Oregon State University, Corvallis, Oregon 97331, USA Department of Physics and Astronomy, University of Maine, 5709 Bennett Hall, Orono, Maine 04469-5709, USA Maine Center for Research in STEM Education, University of Maine, 5727 Estabrooke Hall, Orono, Maine 04469-5727, USA (Received 24 July 2015; published ...

a Department of Business Information Technology, Pamplin College of Business, Virginia Tech, 1007 Pamplin Hall, Blacksburg, VA 24061, United States b Department of Computer Science, Virginia Tech, 114 McBryde Hall, Blacksburg, VA 24061, United States c Department of Accounting and Information Systems, Pamplin College of Business, Virginia Tech, 3007 Pamplin Hall, Blacksburg, VA 24061, United St...

A deep connection between the Hall conductance in realistic situation and a topological invariant is pointed out based on von-Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance has no finite size correction in quantum Hall regime, but a coefficient of induced Chern-Simons term in QED 3 has a small finite size correct...

Let Bn be the set of all n by n Boolean matrices, and let H~ = {A E Bn : Ak is a Hall matrix for every sufficiently large integer k}. We provide upper estimates on the strict Hall exponents of microsymmetric matrices in H~; furthermore, we obtain the maximum value of the strict Hall exponents of symmetric matrices in H~.