Twenty years of distributed port-Hamiltonian systems:A literature review

The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Correlated Exotic States: Fractionalization, Fermi Arcs, Competing Phases

This thesis in the field of condensed matter theory is concerned with various correlated exotic states in different materials. The topic selection is three-fold, covering aspects of graphene, heavy fermion compounds and high-temperature superconductors. In Part I, a symmetrically biased graphene bilayer is considered, which is discussed to host an exciton condensate. It is shown that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. Intervalley mixing occurring in the full lattice model slightly splits the zero modes in energy. This result is supported by an exact numerical diagonalization of the lattice Hamiltonian for a finite-size system. Such a vortex binds an irrational fraction of "axial" charge and obeys fractional exchange statistics. Part II is concerned with heavy fermion materials and discusses the consequences of a momentum-dependent hybridization between the conduction band and the localized electrons, especially in the case where the hybridization function has nodes in momentum space. Such a situation is motivated by experiments, and is in contrast to the commonly studied local hybridization. In the low-temperature regime a highly anisotropic Fermi liquid evolves, for which thermodynamical and optical properties are studied. We find that thermodynamics is dominated by the heavy quasiparticles present in the antinodal direction in momentum space, where the hybridization is strong, while transport is dominated by the behavior of light, nodal quasiparticles. Based on a mean-field approximation, we furthermore study the phase competition between Kondo screening and ordering phenomena induced by intermoment exchange. According to our findings, it is greatly influenced by the interplay of symmetries of the order parameters in momentum space. The results are applicable to CeCoIn5 and other related heavy fermion compounds. Part III discusses the recently observed quantum oscillations in the underdoped regime of cuprates and advertises a new mechanism that requires only finite segments of a Fermi surface to exist. Such a situation is indicated by angle resolved photoemission spectroscopy (ARPES) studies, which exhibit so-called Fermi arcs in the normal state of cuprates. We consider a BCS-like model in the vortex state with a pairing gap producing such Fermi arcs. By exact diagonalization of the gauge transformed real-space Hamiltonian it is shown that the density of states at the Fermi level exhibits an oscillatory behavior