Relativistic quantum Darwinism in Dirac fermion and graphene systems

Kenjiro K. Gomes, Warren Mar, Wonhee Ko +2 more

Feng Mei, Dan-Wei Zhang, Shi-Liang Zhu

Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.

Egon Marx

Ibrahima Sakho

Purpose of the study: The goal of this work is to present a comparative study between the semi-relativistic theory of Sakho and the relativistic theory of Dirac applied to calculations of the eigenvalue of the Hamiltonian fine structure of the hydrogen like systems. The three small perturbative corrections (relativistic mass correction, spin-orbit coupling, and the Darwin term) of the Hamiltonian are considered. Methodology: This research is based on correction of the semi-classical Bohr’s theory on the hydrogen like systems considering the relativistic mass correction by ignoring the electron’s spin. This approach referred to as semi-relativistic theory allows one to express the eigenvalues of the Hamiltonian fine structure to be compared to that from the relativistic wave function of Dirac Main Findings: The research gives the first expression of the quantized energy of hydrogen like systems taking only into account, the relativistic mass correction. This result provides exactly the eigenvalues of the Hamiltonian fine structure predicted from Dirac’s relativistic theory for all the non-degenerated quantum states n2Lj (j = l ± s) of the hydrogen like systems (i.e. 1 2s1/2, 2 2p3/2, 3 2d5/2, 42f7/2, and so on). Novelty/Originality of this study: Theoretical determination of the eigenvalue of the Hamiltonian fine structure predicted from Dirac’s relativistic theory for all the non-degenerated quantum states is obtained with a soft semi-relativistic theory without including in the calculations the spin-orbit coupling and the Darwin term corrections.

Philippe Droz-Vincent