Condensate of Cooper pairs

The theoretical grounds for existence of 2D-SIT which was suggested in [9, 10] appealed to the boson-vortex duality model. It considered the superconducting phase as a condensate of Cooper pairs with localized vortices and the insulating phase as a condensate of vortices with localized Cooper pairs. The theory described only vicinity of the SIT and predicted existence of some critical region on the (T, B)-plane where the behavior of the system was... 

The problematic nature of the melting transition can be illustrated by comparison with other well-known first-order phase transitions, for instance the normal metal-(low T ) superconductor transition. The normal metal-superconductor and melting transitions have similar symptomatic definitions, the former being a loss of resistance to current flow, and the latter being a loss of resistance to shear. However, superconductivity can also be neatly described as a phonon-mediated (Cooper) pairing of electrons and condensation of Cooper pairs into a coherent ground state wave function. This mechanistic description of the normal metal-super-conductor transition has required considerable theoretical effort for its development, but nevertheless boils down to a simple statement, indicat-... 

Most of the superfluid properties of He II (such as the creeping film, second-sound, and so on) have now also been demonstrated for superfluid He. Like He II, the liquid can be described in terms of a two-fluid hydrodynamics. The He superfluid component is associated with the condensate of Cooper pairs, and the normal fluid component with unpaired fermions in excited states. There is a Landau critical velocity representing the onset condition for pair-breaking, about 10 of the size of ul for He II. The two-fluid properties of superfluid He are greatly complicated by its anisotropy, particularly in the case of the... 

One conceptual element of the BCS theory is the formation of - Cooper pairs, namely pairing of -> electrons close to the Fermi level due to a slight attraction resulting from phonon interaction with the crystal lattice. These pairs of electrons act like bosons which can condense into the same energy level. An energy band gap is to be left above these electrons on the order of 10-3 eV, thus inhibiting collision interactions responsible for the ordinary - resistance. As a result, zero electrical resistivity is observed at low temperatures when the thermal energy is lower than the band gap. The founders of the BCS theory, J. Bardeen, L. Cooper, and R. Schrieffer, were awarded by the Nobel Prize in 1972. 

An interesting example of entanglement in condensed matter is represented by the formation of Cooper pairs in conventional superconductors. It is well known that the electron-phonon interaction in metals can lead to formation of collective quantum states of paired electrons with opposite spins and linear momenta [77]. In the simplest quasispin form, the system can be specified by the Hamiltonian [78,79]... 

The specific heat at low temperatures consists of electronic, lattice, magnetic, and hyperfine contributions (see for example, Junod 1996). The electronic contribution in a metal due to the conduction elections is linear in temperature. In a BCS superconductor, the conduction electrons start to condense into Cooper pairs at and the density of unpaired electrons decreases exponentially below this temperature. Hence, at the temperatures of interest in this chapter (i.e., below 4K) the density of unpaired electrons is essentially zero as is expected for the electronic contribution. However, for RBa2Cu30j (R123x) a linear term of the order of y = 3-6 mJ mole was always observed (van der... 

One of the most amazing phenomena in quantum many-particle systems is the formation of quantum condensates. Of particular interest are strongly coupled fermion systems where bound states arise. In the low-density limit, where even-number fermionic bound states can be considered as bosons, Bose-Einstein condensation is expected to occur at low temperatures. The solution of Eq. (6) with = 2/j, gives the onset of pairing, the solution of Eq. (7) with EinP = 4/i the onset of quartetting in (symmetric) nuclear matter. At present, condensates are investigated in systems where the cross-over from Bardeen-Cooper-Schrieffer (BCS) pairing to Bose-Einstein condensation (BEC) can be observed, see [11,12], In these papers, a two-particle state is treated in an uncorrelated medium. Some attempts have been made to include the interaction between correlated states, see [7,13]. 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

Like there always exists a vapor under the water, there are excitations on the ground of any condensate. They appear due to quantum and thermal fluctuations. In classical systems and also at not too small temperatures in quantum systems, quantum fluctuations are suppressed compared to thermal fluctuations. Excitations are produced and dissolved with the time passage, although the mean number of them is fixed at given temperature. Pairing fluctuations are associated with formation and breaking of excitations of a particular type, Cooper pairs out of the condensate. Fluctuation theory of phase transitions is a well developed field. In particular, ten thousands of papers in condensed matter physics are devoted to the study of pairing fluctuations. At this instant we refer to an excellent review of Larkin and Varlamov [15]. 

For nonvanishing A in Eq. (1) the color symmetry is broken. Two of the three quark color degrees of freedom are coupled to bosonic Cooper pairs in the color antitriplet state which can form a Bose condensate.One can combine the chemical potentials Hu, Hd of u and d quarks by introducing Hq = (hu + Hd)/2 and hi = (hu — Hd)/% as the Lagrange multipliers related to, respectively, the quark number density nq and the isospin asymmetry n/. In thermal equilib-... 

The Cooper pairs are bosons, and below a critical Tc (which is affected by both applied pressure and by applied magnetic field) can condense to the same momentum state and wavefunction for all Cooper pairs in the solid these pairs have long-distance phase coherence and are present in all known superconductors. However, the condensation of these Cooper pair bosons is attributed to electron-phonon coupling only for monoatomic and diatomic metals (BCS theory), where the critical temperature Tc depends on isotopic mass. 

In superconductors, the electrons (or holes) close to the Fermi surface can form Cooper pairs [164] of electrons with opposite spin and momentum the electrons (or holes) become coupled to certain lattice phonons. This condensation into a superconducting state occurs below a critical temperature T, affected by pressure and by magnetic field. For external magnetic fields between zero and a... 

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