We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta = 1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the...

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r = 1 if n = 2, 3 and r = 2 + 1 if n ≥ 4. We show that if the square of the Dirac operator on such a manifold has r small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is ...

We show how the port-Hamiltonian formulation of distributed parameter systems, which incorporates energy flow through the boundary of the spatial domain of the system, can be used to model networks of canals and study interconnections of such systems. We first formulate fluid flow with 1-d spatial variable whose dynamics are given by the well-known shallow water equations, with respect to a Sto...

In the conventional QCD sum rule calculation for the πNN coupling beyond the soft-pion limit, there are three distinct Dirac structures, each of which can be used to construct separate sum rule. We point out subtleties in the previous sum rule results, based on one of the Dirac structure, associated with using either the PV or the PS coupling schemes in modeling the phenomenological side. We pr...

Classical model SDcl of the Dirac particle SD is constructed. SD is the dynamic system described by the Dirac equation. For investigation of SD and construction of SDcl one uses a new dynamic method: dynamic disquantization. This relativistic purely dynamic procedure does not use principles of quantum mechanics. The obtained classical analog SDcl is described by a system of ordinary differentia...

Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replicas of the original Dirac cone and Hofstadter butterflies....

It is shown how the geometric framework for distributed-parameter portcontrolled Hamiltonian systems as recently provided in [14, 15] can be adapted to formulate ideal adiabatic fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure introduced in [14] to a Dirac str...