Van der Waals interaction between flux lines in high- superconductors: A variational approach

Abstract

In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance a, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system. PACS. 74.60.Ec Mixed state, critical fields, and surface sheath -74.72.Hs Bi-based cuprates

Interactions and conformational fluctuations in DNA arrays

“…All this is very closely related the analysis of Volmer and Schwartz [28] for the system of magnetic vortex lines in type II superconductors. The only difference is in the conformational energy of a polymer (elastic energy) and a vortex line (tension energy).…”

“…53 and 55 represent the solution to the minimization problem. Very similar equations have already been derived in the case of magnetic vortex arrays [28].…”

“…For a system with a hexagonal local symmetry I follow closely the calculation of Volmer and Schwartz [28] derived for the system of magnetic vortex lines in type II superconductors. Apart from the difference between elastic energies of a vortex line vs. a flexible polymer the two cases are analogous.…”

“…In principle the indices n, m would run through all the positions of the polymers at a certain planar cross section through the nematic but because of the short range nature of the interaction and computational convenience I restrict them to nearest neighbors [28]. K C is of course the elastic modulus of DNA given by K C = k B T L P , where L P is the persistence length.…”

Interactions and conformational fluctuations in DNA arrays

“…where r ⊥ (n,m) (z) is the local displacement of a polymer chain at the (n, m) lattice position perpendicular to the long axis , z, while V r ⊥ (n,m) (z) − r ⊥ (n ,m ) (z) is the interaction potential between different macromolecules at the same value of z. In principle the indices n, m would run through all the positions of the polymers at a certain planar cross section through the nematic but because of the short range nature of the interaction and computational convenience I restrict them to nearest neighbors [28]. K C is of course the elastic modulus of DNA given by K C = k B T L P , where L P is the persistence length.…”