Siam Physics Congress 2016

Time Evolution of Gaussian Wave Packets under Dirac Equation with Fluctuating Mass and Potential

9 Jun 2016, 15:15

15m

Room Th

Oral presentaion Atomic Physics, Quantum Physics, Molecular and Chemical Physics Session XXVII

Speaker

Mr Atis Yosprakob (MU-NECTEC Collaborative Research Unit on Quantum Information, Department of Physics, Faculty of Science, Mahidol University, Phayathai, Bangkok 10400)

Description

Localization of relativistic particles has been of great research interest

over many decades. We investigate the time evolution of a Gaussian wave

packet governed by the one dimensional Dirac equation. The research

methodology consists of analytical approach and numerical simulations

employing the Chebyshev polynomial expansion of the propagation

operator. For the free Dirac equation, we obtain the evolution profiles

analytically in many approximation regimes, and numerical simulations

consistent with other numerical schemes. Interesting behaviors such as

Zitterbewegung and Klein paradox are exhibited. In particular, the

dispersion rate as a function of mass is calculated, and it yields an

interesting result that the super-massive and massless particles both

exhibit no dispersion in free space. For the Dirac equation with random

potential or mass, we obtain the probability profiles of the displacement

distribution when the potential is uniformly distributed. We observe that the

widths of the Gaussian wave packets decrease approximately with the

power law of order $o(r^{-1/2})$ as the randomness strength $r$ increases. This

suggests an onset of localization, but it is weaker than Anderson

localization