Combined electric and magnetic Aharonov–Bohm effects Available to Purchase

Y.

 

Aharonov

and

D.

 

Bohm

, “,”  , – ().

The same effect can be obtained by choosing a smooth non-singular vector potential $A(x,t)$ that is confined in both space and time. Outside the confined region the potential vanishes. Within a certain part of the confined region, it is constant. In the intermediate area it smoothly decays from a constant value to zero. It is only in this region that the electric and magnetic fields do not vanish. Such a potential imposes charge and current densities different from Eqs. (5) and (6), but the setup is still non-radiating. The same combined electric and magnetic Aharonov–Bohm effects are obtained if the two interfering wave packets do not enter (in space-time) the intermediate regions, where $E$ and $B$ are non-trivial. We have used the delta (and step) function(s) to simplify the calculations, specifically those of the charge and current densities.

When treating the sources quantum mechanically, the Coulomb gauge is essential because it describes the back reaction correctly. See

Y.

 

Aharonov

and

J.

 

Anandan

, “,”  , – ().

Note that $j=jl+jt$⁠, where $jl$ is the longitudinal current for which $∇×jl=0$⁠. This standard separation of $j$ does not coincide with $jc$ and $js$ in Eq. (6) as can be verified from Eqs. (9) and (16).

P. M.

 

Morse

and

H.

 

Feshbach

, (, , ), p. .

G. N.

Afanasiev

and

Yu P.

Stepanovsky

, “,”  , – ();

G. N.

 

Afanasiev

, (, , ), pp. –.