Statistical properties of a 1D Bose–Bose mixture at nonzero temperatures

We study finite-temperature, interacting 1D Bose–Bose mixtures using an approach based on the classical field approximation. Extending Castin's method for single-component gases, we present an exact mapping of the mixture onto a system of two distinguishable quantum particles in two dimensions, incorporating leading-order corrections from nonzero Matsubara modes into an effective action. This framework provides an intuitive interpretation via an effective potential while enabling the efficient calculation of finite-temperature correlations, coherence properties, and crossover diagrams for component mixing and separation. Comparing our results with the Mora–Castin method, we demonstrate that this classical field mapping reliably accesses thermal regimes unreachable by Bogoliubov-type theories, offering valuable insights from both theoretical and experimental standpoints.