In the thesis, we numerically study the phase slip fluctuations in low-dimensional superconducting systems using the string method. The string method has been presented as an efficient numerical tool for the study of thermally activated rare events. This numerical approach locates the minimal energy path (MEP) which is the most probable transition pathway connecting two metastable/stable states in configuration space. From the MEP the saddle point is determined and the corresponding energy barrier is also obtained....[ Read more ]

In the thesis, we numerically study the phase slip fluctuations in low-dimensional superconducting systems using the string method. The string method has been presented as an efficient numerical tool for the study of thermally activated rare events. This numerical approach locates the minimal energy path (MEP) which is the most probable transition pathway connecting two metastable/stable states in configuration space. From the MEP the saddle point is determined and the corresponding energy barrier is also obtained.

We first study the phase slips in one-dimensional superconducting wires with nonuniform cross section. The free-energy barrier and the pre-exponential factor associated with the transition rate (resistance) are numerically calculated. We find that even a weak defect can greatly enhance the total rate of transition. Then we study the phase slips in two-dimensional superconducting strips and ultrathin hollow superconducting cylinders. In these two systems, the phase slips may occur via free-energy saddle points of two distinct kinds. The saddle points of the first kind exhibit a one-dimensional order parameter variation described by the Langer-Ambegaokar-McCumber-Halperin theory [Phys. Rev 164, 498 (1967); Phys. Rev B 1, 1054 (1970)]. The saddle points of the second kind exhibit a two-dimensional variation of order parameter with vortex/antivotex involved. Finally, we extend the string method to investigate the critical nuclei for capillary condensation in a slit pore. The application shows the great power of string method in evaluating the critical nuclei in various liquid-vapor phase transitions.