Related papers: Revised Hamiltonian near third-integer resonance a…
In an accelerator, the nonlinear behavior near a horizontal resonance line ($n\nu_x$) usually involves the appearance of stable fixed points (SFPs) in the horizontal phase space, also referred to as transverse resonance island ``buckets"…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…
In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the…
The beam response to an external periodic excitation delivers relevant information about the optics, tune distribution and stability of a circulating beam in a storage ring. In this contribution the horizontal beam response to the…
We study dynamical evolution of a resonant triple system formed by an inner EMRI and an additional outer MBH. The relevant resonant state (\lambda_2-\varpi_1 ~ const) is supported by the relativistic apsidal precession of the inner EMRI,…
Specific velocities of particles circulating in a storage ring can lead to betatron resonances at which static perturbations of the particles' orbit yield large transverse (betatron) oscillations. We have observed betatron resonances in an…
We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions…
In this chapter we give an introduction to the transverse dynamics of the particles in a synchrotron or storage ring. The emphasis is more on qualitative understanding rather than on mathematical correctness, and a number of simulations are…
We study the dynamics of the space debris in regions corresponding to minor resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2, 5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of…
We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system…
We present a family of generalized unitary transformations that simplifies the Hamiltonian for a harmonically trapped two level atom (or ion) interacting with a plane wave laser field. Novel near resonant single as well as double…
The paper gives an overview of the particle dynamics in synchrotrons and storage rings. Both, transverse as well as the longitudinal plane are described in linear approximation. The main emphasis is to give an introduction into the basic…
We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
For resonant slow extraction of accelerated particle beams from synchrotrons, a 3rd order resonance driven by sextupole magnets is commonly used. This note reviews the non-linear particle dynamics under these conditions as described by the…
We report the first direct observation of nonlinear resonance island trapping in a fourth-generation light source with working points far from the excited resonance and examine the nonlinear dynamics and properties of the trapped beam. The…
Based on a novel treatment of near resonances, we introduce a new approximation for the rotating stratified Boussinesq system on three-dimensional tori with arbitrary aspect ratios. The rotation and stratification parameters are arbitrary…
The transition from rotational to discontinuous behavior of the return map of the perturbed oscillators-step system, a paradigm model for a perturbation of a pseudo-integrable Hamiltonian impact system, is studied. The form of the return…
The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…