A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H _(c2). A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 - H/H _(c2)) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.
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机译：提出了一个模型，用于描述当距离大于它们的大小时（温度和磁场）转变点附近的库珀对。该模型的本质如下：Ginzburg-Landau函数以Bose类型的场算子的形式以算子形式编写，因此密度算子的平均值给出了Cooper对的浓度，而相同的Ginzburg-Landau获得Bose冷凝物的表达式。该模型应用于超导板，该板的厚度小于横向磁场在其上临界值H _（c2）附近的一对导体的尺寸。发现了一种新状态，该状态在过渡点附近的一定间隔内比Abrikosov涡态状态在能量上更具优势。在这种状态下，系统的波函数属于分数量子霍尔效应中使用的Laughlin函数的类型（自然，在我们的情况下，作为波塞粒子应用于Cooper对），并且对应于均匀不可压缩的流体。与包含该量平方的涡旋态能量相比，该状态的能量与量的第一幂成正比（1- H / H _（c2））。新状态存在的时间间隔越大，样本越脏。
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