Related papers: A Note on Coadjoint Orbits for Multifermion System…
We characterize the local properties of an optomechanical system comprising the movable mirror of a resonator and its intracavity field, mutually coupled via radiation-pressure. Our approach shows that both the state of the mirror and the…
We study the geometrical structure of the coadjoint orbits of an arbitrary complex or real Lie algebra ${\mathfrak g}$ containing some ideal ${\mathfrak n}$. It is shown that any coadjoint orbit in ${\mathfrak g}^*$ is a bundle with the…
We investigate the structure of the Earth co-orbital region at low eccentricity and low inclination using a semi-analytical model of the 1:1 mean-motion resonance. The dynamics of asteroids in co-orbital motion with the Earth is described…
In this review, analytical results obtained for a wide class of stationary axisymmetric flows in the vicinity of compact astrophysical objects are analyzed, with an emphasis on quantitative predictions for specific sources. Recent years…
I explore computer simulations of the dynamics of small multi-fermion lattice systems. The method is more general, but I concentrate on Hubbard type models where the fermions hop between a small number of connected sites. I use the natural…
Covariant version of the quark-parton model is studied. Dependence of the structure functions and parton distributions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular…
The dynamics of a large quantum spin coupled parametrically to an optical resonator is treated in analogy with the motion of a cantilever in cavity optomechanics. New spin optodynamic phenonmena are predicted, such as cavity-spin…
We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bf C})$ of affine transformations of the complex straight line and apply them to obtain the irreducible unitary representations of this group. These results show…
We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…
A widely-known paradigm in optomechanical systems involves coupling the square of the position of a mechanical oscillator to an electromagnetic field. We discuss how, in the so-called resolved sideband regime, this system allows to simulate…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very-high control accuracy, and…
We introduce notions of continuous orbit equivalence and strong (respective, weak) continuous orbit equivalence for automorphism systems of \'{e}tale equivalence relations, and characterize them in terms of the semi-direct product…
Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been…
In this paper we explain how the cocycle of the momentum map of the action of the affine symplectic group on $\mathbb{R}^{2n}$ gives rise to a coadjoint orbit of the odd real symplectic group with a modulus.
Co-orbital planets have not yet been discovered, although they constitute a frequent by-product of planetary formation and evolution models. This lack may be due to observational biases, since the main detection methods are unable to spot…
We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive.
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
We consider the behavior of Fermi atoms on optical superlattices with two-well structure of each node. Fermions on such lattices serve as an analog simulator of Fermi type Hamiltonian. We derive a mapping between fermion quantum ordering in…