Dirac particle penetration is studied theoretically with Dirac equation in one-dimensional systems. We investigate a one-dimensional system with N barriers where both barrier height and well width are constants random...Dirac particle penetration is studied theoretically with Dirac equation in one-dimensional systems. We investigate a one-dimensional system with N barriers where both barrier height and well width are constants randomly distributed in certain range. The one-parameter scaling theory for nonrelatiyistic particles is still valid for massive Dirac particles. In the same disorder sample, we find that the localization length of relativistic particles is always larger than that of nonrelativistic particles and the transmission coefficient related to incident particle in both cases fits the form T～ exp（-αL）. More interesting, massless relativistic particles are entirely delocalized no matter how big the energy of incident particles is.展开更多
By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distr...By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10174024 and 10474025
文摘Dirac particle penetration is studied theoretically with Dirac equation in one-dimensional systems. We investigate a one-dimensional system with N barriers where both barrier height and well width are constants randomly distributed in certain range. The one-parameter scaling theory for nonrelatiyistic particles is still valid for massive Dirac particles. In the same disorder sample, we find that the localization length of relativistic particles is always larger than that of nonrelativistic particles and the transmission coefficient related to incident particle in both cases fits the form T～ exp（-αL）. More interesting, massless relativistic particles are entirely delocalized no matter how big the energy of incident particles is.
基金supported by National Natural Science Foundation of China under Grant Nos.10675048 and 1068006the Natural Science Foundation of Xianning College under Grant No.KZ0916
文摘By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.
