2011/09/16 by Konstantin V. Grigorishin, K. V. Grigorishin, Grigorishin, K. V. +2 · 1 citation
Computer Science · Engineering · Materials Science · Physics and Astronomy · #Advanced Materials Characterization Techniques #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1109.3677
34 pages, 12 figures
arxiv created 2011/09/16 · openalex publication_date 2011/09/16 · arxiv updated 2011/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The new approach to the microscopic description of the phase transitions starting from the only first principles was developed on an example of the transition normal metal-superconductor. This means mathematically, that the free energy is calculated in the range of temperatures, which includes a point of pase transition, without introducing any artificial parameters similar to an order parameter, but only starting from microscopic parameters of Hamiltonian. Moreover the theorems about connection of a vacuum amplitude with thermodynamics potentials are realized. The functional of a superconductor's free energy in a magnetic field was obtained with help the developed method. The obtained functional is generalization of Ginzburg-Landau functional for the case of arbitrary value of a gap, arbitrary spatial inhomogeneities and nonlocal magnetic response. The explicit expressions for the extremals of this functional were obtained in the low-temperature limit and the high-temperature limit at the condition of slowness of gap's changes.