Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard sphere''-like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in a quite general potential system and will be useful in understanding some other phenomena in mesoscopic physics.Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard sphere''-like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in a quite general potential system and will be useful in understanding some other phenomena in mesoscopic physics.

arXiv:quant-ph/0312200Physical Review AMay 14, 20043 citations

The Aharonov-Bohm effect and scattering theory

Simon N. M. Ruijsenaars

Annals of PhysicsMar 1, 1983226 citations

Aharonov-Bohm effect as a scattering event

Yakir Aharonov, C. K. Au, E. C. Lerner +1 more

The Aharonov-Bohm effect is reconsidered as a scattering event of an electron by a magnetic field confined in an infinite solenoid of finite radius both in the situation where the solenoid is penetrable as well as impenetrable. We next discuss the validity of the Born approximation for the partial-wave scattering amplitudes and explain why for the cylindrically symmetric $(m=0)$ partial wave the first Born approximation fails in the long-wavelength limit or as the radius of the solenoid shrinks to zero.The Aharonov-Bohm effect is reconsidered as a scattering event of an electron by a magnetic field confined in an infinite solenoid of finite radius both in the situation where the solenoid is penetrable as well as impenetrable. We next discuss the validity of the Born approximation for the partial-wave scattering amplitudes and explain why for the cylindrically symmetric $(m=0)$ partial wave the first Born approximation fails in the long-wavelength limit or as the radius of the solenoid shrinks to zero.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMay 15, 198458 citations

(m=0)

partial wave the first Born approximation fails in the long-wavelength limit or as the radius of the solenoid shrinks to zero.