THE LANDAU PROBLEM AND NONCOMMUTATIVE QUANTUM MECHANICS
By J. Gamboa, F. Mendez, M. Loewe, J. C. Rojas. 2001
141 citations recorded by the source corpus.
We explore the conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories. If the potential in noncommutative quantum mechanics is chosen as V=Ωℵ with ℵ defined in the text, then for the value $\tilde\theta=0.22\times 10^{-11}~{\rm cm}^2$ (which measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find different values for $\tilde\theta$ and, therefore, the possible bounds for $\tilde\theta$ should be searched in a physical independent scenario. This last fact could explain the different bounds for $\tilde\theta$ found in the literature.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8bd578ed002f89bc11db8ce1440ac4fc1ae0c6a1
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Citations in the corpus
- The Non-commutative Landau Problem (2002, methodology): “In the standard NC approach [7, 4, 5 ], the Poisson bracket — a contravariant structure — is modified; in the Peierls-type one [1, 2, 3], the coupling is achieved using Souriau’s covariant two-form σ. The two “minimal coupling” rules are hence the duals of each other.”