Related papers: Phase Splitting for Periodic Lie Systems
In the phase space of the integrable Hamiltonian system with three degrees of freedom used to describe the motion of a Kowalevski-type top in a double constant force field, we point out the four-dimensional invariant manifold. It is shown…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
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…
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…
We present a brief overview of the phases and dynamics of ultracold bosons in an optical lattice in the presence of a tilt. We begin with a brief summary of the possible experimental setup for generating the tilt. This is followed by a…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a non-interacting model exhibiting algebraically localized single-particle modes. For this model we find…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
Time-periodic (Floquet) topological phases of matter exhibit bulk-edge relationships that are more complex than static topological insulators and superconductors. Finding the edge modes unique to driven systems usually requires numerics.…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…
Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet…
Phase separation may be driven by the minimization of a suitable free energy ${\cal F}$. This is the case, e.g., for diblock copolimer melts, where ${\cal F}$ is minimized by a steady periodic pattern whose wavelength $\lambda_{GS}$ depends…
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…
In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the 2d plane. The vortices are considered as effective particles and their…
The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
Recently, anomalous Floquet topological phases without static counterparts have been observed in different systems, where periodically driven models are realized to support a winding number of 1 and a pair of edge modes in each quasienergy…
The existence and bifurcation of homoclinic orbits in planar piecewise linear homogeneous systems with two regions separated by a discontinuity boundary are investigated in this paper. In addition, existence of periodic orbits and stability…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…