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By T. Tsuneto, Mikio Nakahara
This graduate-level textual content describes the physics of superconductivity and superfluidity, macroscopic quantum phenomena present in many conductors at low temperatures and in liquid helium four and helium three. within the first a part of the e-book the writer provides the suggest box thought of generalized pair condensation. this can be through an outline of the houses of normal superconductors utilizing BCS idea. The e-book then proceeds with expositions of sturdy coupling thought and the Ginzburg-Landau idea. The impressive homes of superfluid helium three are then defined, for example of a superfluid with inner levels of freedom. fresh subject matters within the box, akin to the copper-oxide hot temperature superconductors and unique superconductivity of heavy fermion platforms are mentioned within the ultimate bankruptcy. This ebook may be of curiosity to graduate scholars and researchers in condensed subject physics, specifically these operating in superconductivity and superfluidity.
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11) always has a bound state solution for a one-dimensional problem however small X may be. 2 Cooper pairs and the BCS ground state Due to the Pauli principle, not only an ideal Fermi gas, but an interacting Fermi system such as electrons in a metal and liquid 3 He, can, at low enough temperatures, be regarded as a system of quasi-particles obeying Fermi statistics; called the Fermi liquid. If there are no phase transitions, the ground state at T = 0 K is a Fermi sphere of quasi-particles. Let aj a be an operator which creates a quasi-particle (which we simply call a particle hereafter) of momentum k and spin a.
0 Fig. 2. The temperature dependence of the energy gap of Pb. The symbol o denotes values obtained by the tunnelling experiment. The solid line is the prediction of the BCS theory. 2 shows the temperature dependence of the energy gap, from which one finds that the mean-field theory reproduces the data very well. 15) The behaviour of A(T) in the vicinity of Tc will be given in the next section. 2 Coherence length The energy scale which characterises a superconducting state is A. 16) 36 BCS theory called the coherence length, is important in the analysis of superconducting phenomena.
Before we close this section, let us write down the free energy. This is given by F(T9 V,n) = - r 1 inTr ( e " ^ ) = - j T 1 E l n (l + e" fe «) + Jf c. 54) The symbol Tr stands for the trace over all possible states of the system. If Eqs. 51) are applicable, Eq. 54) becomes In (l + e" f e a ) - E (£ka - &« + -tvA^k) . 52) is equivalent to the condition that A/c minimises the free energy, namely •^7=0. 56) The matrix elements of A/c and A^ are assumed to be independent when the above variation is taken.