Seminarium Fizyki Materii Skondensowanej

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 intra-species interaction strength J_1, while particles of different types interact with an inter-species 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.