Study Of Thermal Dynamics In Quantum Quasi-One-Dimensional Systems

Fourier's law describes the transport of heat in a macroscopic object.The thermaltransport in low dimensional systems that appears in Fourier's law is fundamental andimportant in understanding the properties of materials.Such a calculation must begrounded upon quantum mechanics with phonons as basic quasi-particles.Whether thethermal transport properties in one-dimensional (1D)are ruled by the Fourier's law? Lotsof works have been done to answer this answer.We studied the thermal transport inFermi-Pasta-Ulam (FPU)chains with the extended Ford-Kac-Mazur (FKM)formulism.The thermal properties in FPU chains with Frenkel-Kontorova (FK)on-site potential arealso studied using fourth-order Runge-Kutta algorithm.The main work is included asfollows:1.Thermal transport in 1 D FPU chains using the extended quantum FKM formalism.It is found that the coupling of the central chain and the reservoirs is important for thethermal transport in one-dimensional chains.When the coupling strength between thecentral chain and the reservoirs is strong,the spectra of heat current are continuous.Forweak coupling conditions,the spectra of heat current are discrete according the phononlocalization at the boundary.The numerical results have qualitatively shown that the heat current varies with thesize of system in terms of J∝1/N^1/2when the 1D chain is connected with Landauer reservoirs.For the Langevin case,relation of J and N is more complex.It is indicated thatthe nonlinear effects result in phonon localization.The phonons in the 1D chain arescattering by the nonlinearity.It is interesting that the local kinetic energy displays even-odd effects due to theinterference of thermal waves.When the temperatures of the left and right reservoirs areequal,there are stable steps in the central chains with even system size.However,thestable steps do not exist when the system size is odd.The stable steps can be treated as thelocal temperature of the 1D chain with finite system size.The fluctuations anddistributions of the local kinetic energy are different for odd or even system size.Thisphenomenon is a disordered odd-even effect.However,there are no stable steps in thedisordered chain.This effect is different with the odd-even effect in the ordered chain.2.Thermal transport in 1D FPU-FK chains using fourth-order Runge-Kutta algorithm.It was found that the local equilibrium of the FPU-FK lattice was well established.Especially,temperature gradient scales behave as N^-1and the heat conductivityκdivergeswith system size asκ∝JN∝N^αwithα=0.44±0.01,displaying a kind of universalfeatures.