Related papers: Extracting Multidimensional Phase Space Topology f…

For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a…

We consider ultracold matter of spin-2 atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian…

We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…

When placed in parallel magnetic and electric fields, the electron trajectories of a classical hydrogen atom are chaotic. The classical escape rate of such a system can be computed with classical trajectory Monte Carlo techniques, but these…

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…

We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of…

Based on the classical and quantum ergodic hierarchy, a framework for mixed systems with a phase space composed by two uncorrelated integrable and chaotic regions is presented. It provides some features of mixed systems connecting the…

We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…

We study the crossover between liquid and solid electron phases in a two-dimensional harmonic trap as the density is progressively diluted. We infer the formation of geometrically ordered phases from charge distributions and pair…

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…

We theoretically investigate the orbital effects of an in-plane magnetic field on the spectrum of a quantum dot embedded in a two-dimensional electron gas (2DEG). We derive an effective two-dimensional Hamiltonian where these effects enter…

Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…

We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence…

We study the evolution of spin-orbital correlations in an inhomogeneous quantum system with an impurity replacing a doublon by a holon orbital degree of freedom. Spin-orbital entanglement is large when spin correlations are…

The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…

In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems $H$ whose potential models the motion of elliptic galaxies.