Superconductivity, potentialities

Ideally a standard cell is constmcted simply and is characterized by a high constancy of emf, a low temperature coefficient of emf, and an emf close to one volt. The Weston cell, which uses a standard cadmium sulfate electrolyte and electrodes of cadmium amalgam and a paste of mercury and mercurous sulfate, essentially meets these conditions. The voltage of the cell is 1.0183 V at 20°C. The a-c Josephson effect, which relates the frequency of a superconducting oscillator to the potential difference between two superconducting components, is used by NIST to maintain the unit of emf. The definition of the volt, however, remains as the Q/A derivation described. 

Superconductivity. One potential future use of vanadium is in the field of superconductivity. The compound V Ga exhibits a critical current at 20 T (20 X lO" G), which is one of the highest of any known material. Although niobium—zirconium and Nb Sn have received more attention, especiahy in the United States, the vanadium compound is being studied for possible future appHcation in this field since V Ga exhibits a critical temperature of 15.4 K as opposed to 18.3 K for Nb Sn. 

Electric utilities can anticipate peak demands and be prepared to meet them. On the other hand, there arc short-term fluctuations in the power levels that a utility cannot anticipate but must handle quickly. Superconducting magnetic energy storage (SMES) is a technology that has potential for meeting both anticipated peak demands and those requiring quick response. 

Metals and semiconductors are electronic conductors in which an electric current is carried by delocalized electrons. A metallic conductor is an electronic conductor in which the electrical conductivity decreases as the temperature is raised. A semiconductor is an electronic conductor in which the electrical conductivity increases as the temperature is raised. In most cases, a metallic conductor has a much higher electrical conductivity than a semiconductor, but it is the temperature dependence of the conductivity that distinguishes the two types of conductors. An insulator does not conduct electricity. A superconductor is a solid that has zero resistance to an electric current. Some metals become superconductors at very low temperatures, at about 20 K or less, and some compounds also show superconductivity (see Box 5.2). High-temperature superconductors have enormous technological potential because they offer the prospect of more efficient power transmission and the generation of high magnetic fields for use in transport systems (Fig. 3.42). 

Practical constraints prevent this technique from living up to its potential, even in this, the era of the superconducting probe. Until sensitivity improves by at least another order of magnitude, the INADEQUATE experiment will remain just that - inadequate by name and by nature. 

In contrast, within (p-EPYNN)[Ni(dmit)2], first synthesized in 1996 [79], it has been proven that spin-ladder chains of the Ni(dmit)2 moiety coexist with the ferromagnetic one-dimensional chain of the p-EPYNN radical cation. Spin-ladders are of interest because of their potential applications in the area of quantum magnets and because it has been predicted that holes doped into even-leg ladders may pair and possibly superconduct [90-92]. 

In refs (Kim,2004 Kim, 2005) we take one step further estimating corrections to the Gaussian effective potential for the U(l) scalar electrodynamics where it represents the standard static GL effective model of superconductivity. Although it was found that, in the covariant pure (f)4 theory in 3 + 1 dimensions,corrections to the GEP are not large (Stancu,1990), we do not expect them to be negligible in three dimensions for high Tc superconductivity, where the system is strongly correlated. 

At low temperatures, matter will undergo a transition to a color-superconducting state, with a different quasiparticle structure than presumed in our quasiparticle approach. Nonetheless, pairing affects the thermodynamic bulk properties only at the relative order of 0(A2/fi2), where the estimated gap A < 100 MeV is comfortably smaller than the chemical potential. Therefore, our equation of state is a reasonable approximation even at small temperatures (maybe except for the pressure where it becomes very small). 

I will focus here on the two basic effective Lagrangians developed for color superconductivity. More specifically the Lagrangian for the color flavor locked phase (CFL) of QCD at high chemical potential and the 2 flavor color superconductive effective Lagrangian. 

A color superconducting phase is a reasonable candidate for the state of strongly interacting matter for very large quark chemical potential [16-20], Many properties of such a state have been investigated for two and three flavor QCD. In some cases these results rely heavily on perturbation theory, which is applicable for very large chemical potentials. Some initial applications to supemovae explosions and gamma ray bursts can be found in [21] and [22] respectively, see also [27], The interested reader can find a discussion of the effects of color superconductivity on the mass-radius relationship of compact stars in [45]... 

For Nf = 3 light flavors at very high chemical potential dynamical computations suggest that the preferred phase is a superconductive one and the following ansatz for a quark-quark type of condensate is energetically favored ... 

We have shown that the vector mesons in the CFL phase have masses of the order of the color superconductive gap, A. On the other hand the solitons have masses proportional to F%/A and hence should play no role for the physics of the CFL phase at large chemical potential. We have noted that the product of the soliton mass and the vector meson mass is independent of the gap. This behavior reflects a form of electromagnetic duality in the sense of Montonen and Olive [29], We have predicted that the nucleon mass times the vector meson mass scales as the square of the pion decay constant at any nonzero chemical potential. In the presence of two or more scales provided by the underlying theory the spectrum of massive states shows very different behaviors which cannot be obtained by assuming a naive dimensional analysis. 

To complete our discussion of non-relativistic superfluids let us briefly mention some of the alternatives to the LOFF and DFS phases. One possibility is that the system prefers a phase separation of the superconducting and normal phases in real space, such that the superconducting phase contains particles with the same chemical potentials, i.e. is symmetric, while the normal phase remains asymmetric [20, 21],... 

In a superconducting system, when one increases the temperature at a given chemical potential, thermal motion will eventually break up the quark Cooper pairs. In the weakly interacting Bardeen-Copper-Schrieffer (BCS) theory, the transition between the superconducting and normal phases is usually of second order. The ratio of the critical temperature TcBCS to the zero temperature value of the gap AbGS is a universal value [18]... 

The high-density phases of QCD at low temperatures can be realized in rotating compact stars - pulsars. Therefore, the observational data from pulsars could provide potentially important information on the state of matter at super-nuclear densities, in particular the superconducting quark matter. 

The Fourier component of the density of the thermodynamic potential (thermodynamic potential per unit volume V) in the superconducting quark matter with the diquark pairing can be written in the following form [12, 16], cf. also [1,11],... 

Contribution of pairing fluctuations to the specific heat in the hadron shell is minor for the case of the neutron pairing due to a small value of Tc < IMeV compared to the value of the neutron chemical potential f//, > 50 MeV). Therefore in the neutron channel fluctuations of the gap are relevant only in a very narrow vicinity of the critical point. However this effect might be not so small for protons, for which the chemical potential is of the order of several MeV, whereas the gap is of the order of one MeV. Therefore it seems that fluctuations may smear the phase transition in a rather broad vicinity of the critical point of the proton superconductivity. 

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

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