Related papers: Average amplitude and phase detuning near driven 3…
A breathing mode in a Hamiltonian system is a function on the phase space whose evolution is exactly periodic for all solutions of the equations of motion. Such breathing modes are familiar from nonlinear dynamics in harmonic traps or…
The dynamics of nanomechanical resonators driven by both low- and high-frequency signals is studied. Considering, as an example, resonators made of a doubly-clamped beam with magnetomotive driving, it is shown that three-frequency…
We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to…
The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is…
We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part…
In this work, average Hamiltonian theory is used to study selective excitation in a spin-1/2 system evolving under a series of small flip-angle $\theta-$pulses $(\theta\ll 1)$ that are applied either periodically [which corresponds to the…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary…
The averaged resonant equations of motion for the planar circular restricted three-body problem are solved on the linearization basis taking into account also non-gravitational effects. The averaged resonant equations are derived from…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The microresonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of…
Pion-kaon ($\pi K$) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $\pi K$ scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in…
We investigate parametric autoresonance: a persisting phase locking which occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and…
We analyze two coupled quantum oscillators in a common Lorentzian environment and control them by detuning (temporarily shifting) their frequencies. The reduced dynamics are solved exactly, without Born or Markov approximations, by…
The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also…
A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…
A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the…
This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely…
In three-dimensional electromagnetic configurations that result from unstable resistive tearing modes particles can efficiently be accelerated to relativistic energies. To prove this resistive magnetohydrodynamic simulations are used as…