General Analytical Method of Kibble-Zurek Mechanism for Exact Prediction of Topological Defects Production

In the field of non-equilibrium phase transitions, the Kibble-Zurek mechanism (KZM) is undoubtedly an important discovery, pointing out that some universal scaling rules are applied to a wide range of physical systems from quantum to the cosmos in complex non-equilibrium continuous phase transitions. However, except for some scaling relations in specific cases, the algebraic-based KZM can not provide further details on the topological defect generation laws. In this work, we propose an analytical-based KZM that can accurately predict topological defect generation for a given quenching condition. Compared with the conventional KZM, our theory is more accurate and more widely applicable, especially in non-linear quenching conditions and inhomogeneous structural systems, where it has more obvious advantages. Our work reveals a fundamental and intrinsic mechanism in non-equilibrium phase transitions, blazing a new trail for accurate description and manipulation of topological defect generation.