Aharonov-Bohm Effect


The activities of the group in this field are focussed on a comprehensive investigation of the AB effect itself, QED processes in the AB magnetic field and the AB effect in atom interferometry.

Our results include:

  • The investigation of the QED processes in a string magnetic field:

Bremsstrahlung of relativistic electrons scattered by a magnetic string (J. Audretsch , U. Jasper, V.D. Skarzhinsky, Phys. Rev. D 53, p. 2178 (1996), preprint: hep-th/9709133) and electron-positron pair production by photons of high energies in the string magnetic field (V.D. Skarzhinsky, J. Audretsch and U. Jasper, Phys. Rev. D 53, p. 2190 (1996), preprint: hep-th/9709134) were considered. The possible experimental testing of the effects was discussed in the papers (J. Audretsch, V. D. Skarzhinsky, Foundations of Physics, 28, p. 777 (1998), preprint: hep-th/9709095; Physics of Particles and Nuclei, 29, No. 3, p. 278 (1998)). The influence of finite size of the magnetic tube on the relativistic electron scattering was also studied ( V. D. Skarzhinsky, J. Audretsch , J. Physics, A: Math. Gen. 30, p. 7603 (1997), preprint: hep-th/9709086).

  • Investigation of the scattering of neutral polarizable atoms in electromagnetic fields:

The effective Lagrangian for polarized atoms scattered by electrically charged wire placed in a homogeneous magnetic field contains an AB potential in addition to an singular 1/rho^2 attractive potential of dipole interaction with the charged wire. The scattering amplitude was calculated for the practically important case that atoms are totally absorbed if they reach the surface of the wire (J. Audretsch, V.D. Skarzhinsky, Phys. Lett. A 241, 7-13 (1998), preprint: quant-ph/9802064). It has been shown that the AB amplitude dominates other contributions in the scattering at small angles. The absorption causes a modulation of the AB amplitude by narrow peaks and dips, resulting in a thin structure of the AB peak. The role of absorption for the AB scattering of charged particles as well as for the scattering of polarizable atoms by an charged wire placed in a homogeneous magnetic field was investigated in detail (J. Audretsch, V.D. Skarzhinsky, Phys. Rev. A 60, 1854-1863 (1999), preprint: quant-ph/9901066).

Elastic scattering and bound states in the AB potential superimposed by the attractive 1/rho^2 potential were treated. This problem is directly connected with the scattering of polarizable atoms. The boundary conditions for solutions of the Schrödinger equations are specified in such a way that the Hamiltonian of the system is self-adjoint. It was shown that the solutions are not uniquely fixed but depend on open parameters. The scattering cross section was calculated and the energy spectrum of bound states was obtained (to be published in J.Phys. A, preprint: quant-ph/0004065).

The absorption problem in singular attractive potentials was investigated and possible criteria for selection of solutions of wave equations were considered (the talk on Int.Conference "Quantization, Gauge Theory and Strings", Moscow, June 5-10, 2000, to be published). It was shown that different models of absorption, from almost elastic scattering up to the total absorption, can be realized by a special choice of the solutions.