content_image/431862.jpg content_image/431864.jpg content_image/431861.jpg content_image/431857.jpg content_image/431858.jpg content_image/431859.jpg content_image/431860.jpg content_image/431863.jpg content_image/431865.jpg
would only renormalize the electron transmission through the potential barrier separating two potential wells. That means that the electron-electron interaction would not essentially change our results. 

Finally, we relate our results to the paper by Kohn [17], which defines the insulating state as a property of the many- body ground state (see also the review by Resta [32]). Kohn’s paper contains a discussion implicitly admitting the existence of a negligibly small persistent current in the insulating ring [see the discussion of equations (2.23) - (2.31) in that work]. Kohn points out the exponential localization of the electron states in the ring. However, he clearly states by writing his equation (2.30), that the current is zero only approximately. Just this negligibly small current is calculated in our paper. Surprisingly, it can be of measurable size. 

This work was supported by grants APVV-51-003505 and VVCE-0058-07 from the Grant Agency APVV and by grants VEGA-2/0633/09 and VEGA-2/0206/11 from the Grant Agency VEGA. We thank Pavol Quittner for important help with the mathematical derivation in Appendix D. 

## APPENDIX A: DERIVATION OF EQUATION (30) FROM EQUATION (28) 

We start by writing Eq. (28) as 

Using substitution j ′ = Ns + j , where s = 0 , 1 , 2 , . . . and j = 0 , 1 , . . . ( N − 1) , we obtain 

<img src='content_image/431862.jpg'>

Assuming that N is odd we rewrite Eq. (99) as 

<img src='content_image/431864.jpg'>

## ACKNOWLEDGEMENTS 

<img src='content_image/431861.jpg'>

where M = Int( N/ 2) . Equation (100) can be rewritten as 

<img src='content_image/431857.jpg'>

Utilizing definition (29) we find from Eq. (101) the result 

<img src='content_image/431858.jpg'>

where 

<img src='content_image/431859.jpg'>

We have sofar assumed odd N . For even N , derivation is similar and we find again the results (101) and (102), except that for j = N/ 2 we have instead of Eqs. (102) the equations 

<img src='content_image/431860.jpg'>

Equation (101) coincides with Eq. (30). 

## APPENDIX B: VARIOUS FORMS OF EQUATION (60) 

We first assume odd N . We can rewrite Eq. (60) as 

<img src='content_image/431863.jpg'>

where M = Int(N / 2) . Further, 

<img src='content_image/431865.jpg'>

