This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finitedimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of f...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described byK is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’s...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described byK is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’s...

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described by K is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described by K is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’...

Abstract: The problem of discrete-time modeling of the lumped-parameter Hamiltonian systems is considered for engineering applications. Hence, a novel gradient-based method is presented, exploiting the discrete gradient concept and the forward Euler discretization under the assumption of the continuous Hamiltonian model is known. It is proven that the proposed discrete-time model structure defi...

We consider a linear Hamiltonian Difference System for the so-called singular case so that discrete Sturm]Liouville Equations of higher order are included in our theory. We introduce the concepts of focal points for matrix-valued and generalized zeros for vector-valued solutions of the system and define disconjugacy for linear Hamiltonian Difference Systems. We prove a Reid Roundabout Theorem w...