A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and non-Abelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.

Using the scattering approach to the construction of Non-Equilibrium Steady States proposed by Ruelle we study the transport properties of systems of independent electrons. We show that Landauer–Büttiker and Green-Kubo formulas hold under very general conditions.

Abstract We introduce a model for charge and heat transport based on the Landauer-Bu"ttikerscattering approach. The system consists of a chain of N quantum dots, each of thembeing coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can bedescribed by any of the standard physical distributions: Maxwell-Boltzmann, FermiDirac and Bose-Einstein. In the linear response regime, and under some assumptions,we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (TL, uL) and (TR, uR), andadjust the parameters (Ti, ui), for i = 1,..., N, so that the net electric and heat cur-rents through all the intermediate reservoirs vanish. This leads to expressions for the temperature and chemical potential profiles along the system, which turn out to beindependent of the distribution describing the reservoirs. We also determine the electric and heat currents flowing through the system and present some numerical results,using random matrix theory, showing that the statistical average currents are governed by Ohm and Fourier laws. Mathematics Subject Classification 80A20, 81Q50, 81U20, 82C70 Keywords Quantum transport; Quantum dots; Landauer-Bu"ttiker scattering approach;Onsager relations; Entropy production; Random matrix theory; Ohm and Fourier laws

We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (TL, µL) and (TR, µR), and adjust the parameters (Ti, µi), for i = 1,..., N, so that the net electric and heat currents through all the intermediate reservoirs vanish. This leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that the statistical average currents are governed by Ohm and Fourier laws.