Excited states in Richardson pairing model: `probabilistic' approach

Richardson equations can be mapped on the classical electrostatic problem in two dimensions. We have recently suggested a new analytical approach to these equations in the thermodynamical limit, which is based on the `probability' of the system of charges to be in a given configuration at the effective temperature equal to the interaction constant. In the present paper, we apply this approach to excited states of the Richardson pairing model. We focus on the equally-spaced situation and address arbitrary fillings of the energy layer, where interaction acts. The `partition function' for the classical problem on the plane, which is given by Selberg-type integral, is evaluated exactly. Three regimes for the energy gap are identified, which can be treated as the dilute regime of pairs, BCS regime, and dilute regime of holes.Comment: 14 pages, 1 figur

Effect of thermal fluctuations on spin degrees of freedom in spinor Bose-Einstein condensates

We consider the effect of thermal fluctuations on rotating spinor F=1 condensates in axially-symmetric vortex phases, when all the three hyperfine states are populated. We show that the relative phase among different components of the order parameter can fluctuate strongly due to the weakness of the interaction in the spin channel. These fluctuations can be significant even at low temperatures. Fluctuations of relative phase lead to significant fluctuations of the local transverse magnetization of the condensate. We demonstrate that these fluctuations are much more pronounced for the antiferromagnetic state than for the ferromagnetic one.Comment: 5 pages, 2 figures; final version, accepted for publication in Phys. Rev.

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.Comment: 9 pages, 1 figure; accepted for publication in Eur. Phys. J.

Little-Parks effect in a superconducting loop with magnetic dot

We have studied the nucleation of superconductivity in a mesoscopic Al loop, enclosing magnetic dot with perpendicular magnetization. The superconducting phase boundary Tc(B), determined from transport measurements, is asymmetric with respect to the polarity of an applied magnetic field. The maximum critical temperature has been found for a finite applied magnetic field, which is antiparallel to the magnetization of the dot. Theoretical phase boundary shows a good agreement with the experimental data.Comment: to be published in Phys. Rev. B - Brief Report