We consider a two-component log gas consisting of $N$ particles confined in a one-dimensional harmonic trap, where the particles interact via a repulsive logarithmic potential. Unlike the previously studied cases involving a single particle species, the present system consists of two types of particles. Particles of the same type interact with an intraspecies interaction strength $J_1$, while particles of different types interact with an interspecies interaction strength $J_2$. Furthermore, we consider a fraction $f(<1)$ of the particles belongs to one type, while the remaining fraction $(1-f)$ are of the other type. We show that this two-component system in thermal equilibrium can be approximately mapped to a single-component system with an effective interaction strength $J_f=J_1(1-2f+2f^2)+J_2(2f-2f^2)$. This mapping is supported by results for the average density profile and the spacing distribution obtained via Monte Carlo simulations at low temperature.

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• Classical statistical mechanics
• Effective field theory
• Particle interactions
• Continuum particle models