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Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we… (More)

- Y Morita, K Ishibashi, Y Hatsugai
- 1999

Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is explored numerically. The regime is closely related to the continuum model. The change of the Hall conductance and the… (More)

- Y Hatsugai, K Ishibashi, Y Morita
- 1999

The Hall conductance σ xy of two-dimensional lattice electrons with random potential is investigated. The change of σ xy due to randomness is focused on. It is a quantum phase transition where the sum rule of σ xy plays an important role. By the string (anyon) gauge, numerical study becomes possible in sufficiently weak magnetic field regime which is… (More)

- Y S Wu, Y Yu, Y Hatsugai, M Kohmoto
- 1998

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of… (More)

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