A set of simple theoretical criteria was established for the occurrence of the Meissner effect in a many-electron system. The criteria are of a qualitative nature and involve only the single- and two-particle excitations of the system. (auth)
The study of the entanglement properties of systems of N fermions has attracted considerable interest during the last few years. Various separability criteria for pure states of N identical fermions have been recently discussed but, except for the case of two-fermions systems, these criteria are difficult to implement and are of limited value from the practical point of view. Here we advance simple necessary and sufficient separability criteria for pure states of N identical fermions. We found that to be identified as separable, a state has to comply with one single identity involving either the purity or the von Neumann entropy of the single-particle reduced density matrix. These criteria, based on the verification of only one identity, are drastically simpler than the criteria discussed in the recent literature. We also derive two inequalities verified, respectively, by the purity and the entropy of the single-particle, reduced density matrix, which lead to natural entanglement measures for N -fermion pure states. Our present considerations are related to some classical results from the Hartree-Fock theory, which are here discussed from a different point of view in order to clarify some important points concerning the separability of fermionic pure states.
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if q>3, where q is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.
A general analysis of Meissner effect and spin susceptibility of a uniform superconductor in an asymmetric two-component fermion system is presented in nonrelativistic field theory approach. We found that the pairing mechanism dominates the magnetization property of superconductivity and the asymmetry enhances the paramagnetism of the system. At the turning point from BCS to breached pairing superconductivity, the Meissner mass squared and spin susceptibility are divergent at zero temperature. In the breached pairing state induced by chemical potential difference and mass difference between the two kinds of fermions, the system goes from paramagnetism to diamagnetism, when the mass ratio of the two species increases.