We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-abelian gauge groups, we propose a conjecture ...

Port based network modeling of complex lumped parameter physical systems naturally leads to a generalized Hamiltonian formulation of its dynamics. The resulting class of open dynamical systems are called “Port-Hamiltonian systems” [12] which are defined using a Dirac structure, the Hamiltonian and dissipative elements. This formulation has been successfully extended to classes of distributed pa...

We study the effects of insulating oxides in their crystalline forms on the energy band structure of monolayer and bilayer graphene using a first principles density functional theory based electronic structure method and a local density approximation. We consider the dielectric oxides SiO(2) (α-quartz) and Al(2)O(3) (alumina or α-sapphire), each with two surface terminations. Our study suggests...

I am not interested in proofs. I am only interested on how Nature works P.A.M. Dirac One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or " front form " dynamics, which plays a crucial role in string theory and in elucidating the fin...

Graphene is a two-dimensional material defined as a planar honeycomb lattice of close-packed carbon atoms, where the electrons exhibit a linear dispersion near Dirac K points and behave as massless Dirac fermions. However, the valence and conduction bands in an AB stacked graphene bilayer split into two parabolic branches near the K point originating from the interaction of p electrons, and the...