Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System

– We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient is made using the quantum master equation, and the mixing properties and the convergence of the Green-Kubo formula are investigated when the number of spin increases. We find that the autocorrelation function in the Green-Kubo formula decays as ∼ t to a finite value which vanishes rapidly with the increase of the system size. As a result, the Green-Kubo formula converges to a finite value in the thermodynamic limit. These facts strongly support the realization of Fourier heat law in a quantum system. The Fourier heat law is one of the most important properties in the nonequilibrium thermodynamics. It states that the heat current per volume is proportional to the thermal gradient. Microscopic dynamical origin for the realization of Fourier heat law has been actively studied using many Hamiltonian systems [1, 2, 3]. In the complete harmonic chain, no global thermal gradient appears, and local equilibrium is not realized, which are attributed to the lack of scattering between modes [1, 4]. In an isotropic d-dimensional classical Fermi-Pasta-Ulam (FPU) system which has the nonlinear potential term, the mixing property satisfies because the auto-correlation function of the energy current roughly decays as t. However due to its slow relaxation of the current fluctuation, the Green-Kubo formula diverges in the oneand two-dimensional systems which causes an anomalous energy transport [2, 5]. In low dimensional systems, most of the problems preventing a normal thermal conduction arises from a slow fluctuation of energy current, including the failure of mixing property. This situation is also the case in the quantum systems. Many integrable one-dimensional systems show the failure of mixing property. In the isotropic Heisenberg chain, the energy current operator commutes with the Hamiltonian, which trivially causes the failure of mixing property and the abnormal energy transport [6]. The recent experiments confirmed a such ballistic heat transport in Sr2CuO3 [7] and CuGeO3 [8] which are described by the isotropic Heisenberg chain. In this paper, we study how the normal thermal conduction in a one-dimensional quantum system is realized in microscopic point of view. In quantum systems, the dynamical origins of