Dual families of noncommutative quantum systems
We demonstrate how a one parameter family of interacting noncommuting Hamiltonians, which are physically equivalent, can be constructed in noncommutative quantum mechanics. This construction is carried out exactly (to all orders in the noncommutative parameter) and analytically in two dimensions for...
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| Veröffentlicht in: | Physical review. D, Particles and fields Particles and fields, 2005-04, Vol.71 (8), Article 085005 |
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| container_title | Physical review. D, Particles and fields |
| container_volume | 71 |
| creator | Scholtz, Frederik G. Chakraborty, Biswajit Gangopadhyay, Sunandan Hazra, Arindam Ghosh |
| description | We demonstrate how a one parameter family of interacting noncommuting Hamiltonians, which are physically equivalent, can be constructed in noncommutative quantum mechanics. This construction is carried out exactly (to all orders in the noncommutative parameter) and analytically in two dimensions for a free particle and a harmonic oscillator moving in a constant magnetic field. We discuss the significance of the Seiberg-Witten map in this context. It is shown for the harmonic oscillator potential that an approximate duality, valid in the low-energy sector, can be constructed between the interacting commutative and a noninteracting noncommutative Hamiltonian. This approximation holds to order 1/B and is therefore valid in the case of strong magnetic fields and weak Landau-level mixing. |
| doi_str_mv | 10.1103/PhysRevD.71.085005 |
| format | Article |
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| identifier | ISSN: 1550-7998 |
| ispartof | Physical review. D, Particles and fields, 2005-04, Vol.71 (8), Article 085005 |
| issn | 1550-7998 0556-2821 1550-2368 1089-4918 |
| language | eng |
| recordid | cdi_osti_scitechconnect_20709109 |
| source | American Physical Society Journals |
| subjects | COMMUTATION RELATIONS DUALITY HAMILTONIANS HARMONIC OSCILLATORS MAGNETIC FIELDS PHYSICS OF ELEMENTARY PARTICLES AND FIELDS POTENTIALS QUANTUM FIELD THEORY QUANTUM MECHANICS |
| title | Dual families of noncommutative quantum systems |
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