Quantum statistical analysis of superconductivity, fractional quantum Halleffect, and aromaticity

The phenomena of superconductivity and fractional quantum Hall effect (FQHE ) as well as the well-known chemical concepts of aromaticity and antiaromat icity are analyzed on the basis of quantum statistical considerations. We s uggest that the superconducting transition is caused by a first-order inter action between the charge carriers which does not necessarily involve a sec ond-order coupling of the electron-phonon type. For molecular model systems it is demonstrated that the formation of superconducting Cooper pairs can lead to an attenuation of destabilizing quantum constraints of the intersit e type, i.e., constraints due to the Pauli antisymmetry principle (PAP). We suggest that this attenuation is the driving force for the superconducting transition. Such a reduction of the PAP influence on the quantum ensemble is also the key element of the present explanation of the FQHE. Analogies b etween the superconducting transition and the plateaus in the Hall conducta nce are emphasized. Both phenomena can be interpreted in terms of an electr onic phase transition which shifts the original fermionic (fe) system towar ds a hard core bosonic (hcb) boundary. hcb ensembles are characterized by o n-site anticommutativity and intersite commutativity. The collective solid- state phenomena superconductivity and FQHE are correlated with the popular chemical concepts of aromaticity and antiaromaticity. Numerical results for the superconducting pairing are derived by the two-parameter Hubbard Hamil tonian. In order to express physically transparent interrelations between f e and hcb ensembles, the so-called statistical transmutation is adopted. Ar guments on the basis of experimental results are summarized which support t he present PAP-driven superconducting pairing formalism. (C) 2000 John Wile y & Sons, Inc.