Quantum liquids of particles with generalized statistics

Abstract

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and $f$-sum rules.