Levinson theorem for Aharonov-Bohm scattering in two dimensions
نویسندگان
چکیده
منابع مشابه
Levinson theorem for Aharonov-Bohm scattering in two dimensions
In 1949 Levinson 1 established one of the most beautiful results of scattering theory: the Levinson theorem sets up a relation between the number of bound states, Nl , in a given lth partial wave and the phase shift l k : namely, l 0 − l = Nl . Ten years later, in 1959, Aharonov and Bohm 2 discovered the global properties of the magnetic flux. Nowadays the Aharonov-Bohm AB effect is often invol...
متن کاملGeneralized Levinson theorem for singular potentials in two dimensions
The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states Nm b in a given mth partial wave is related to the phase shift dm(k) and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form n/r and inverse square tail at ...
متن کاملRelativistic Scalar Aharonov-Bohm Scattering
We discuss the scattering of relativistic spin zero particles by an infinitely long and arbitrarily thin solenoid. The exact solution of the first-quantized problem can be obtained as a mimic of the nonrelativistic case, either in the original Aharonov-Bohm way or by using the Berry’s magnetization scheme. The perturbative treatment is developed in the Feshbach-Villars two-component formalism f...
متن کاملUnitarity of the Aharonov-Bohm Scattering Amplitudes
We discuss the unitarity relation of the Aharonov-Bohm scattering amplitude with the hope that it distinguishes between the differing treatments which employ different incident waves. We find that the original Aharonov-Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other hand,...
متن کاملRelativistic Corrections to the Aharonov-Bohm Scattering
We determine the |p|/m expansion of the two body scattering amplitude of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle amplitude reduces to the Aharonov-Bohm one is restricted to the leading, nonrelativistic, order. The sub...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review A
سال: 2006
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.74.052703