2021/11/12 by Xiaosen Han, Kexin Zhang, Han, Xiaosen +1
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.2111.06600
In this paper, the two-component Ginzburg-Landau (TCGL) model, which is an important research object in mathematics and physics of two scalar fields with U(1)× U(1) symmetry, is studied in detail by the shooting method and the fixed point theorem, which contains two cases: single vacuum expectation value (1VEV) and two vacuum expectation values (2VEV). This represents two different physical states: superconductivity-normal state and superconductivity superconductivity state, and we prove the existence, uniqueness, asymptotic properties and quantization of the solutions to these two boundary value problems.