Related papers: Nonlinear normal modes in electrodynamic systems: …
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…
Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…
A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector…
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the…
We propose a model that, accounting for the intrinsic non-linearity of the electronic system, is able to rationalize steady-state electronic and vibrational spectra of polar chromophores in solution, as well as time-resolved experiments.
In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon qubits in the…
The paper explores a theoretical possibility of resonant amplification of electromagnetic modes generated by a nonlinear effect in Euler-Heisenberg electrodynamics. Precisely, we examine the possibility of the amplification for the third…
Non-perturbative phenomena in four-wave mixing spectra of semiconductors are studied using the exact solution of a widely used phenomenological non-linear equation of motion of the exciton polarization. It is shown that Coulomb interaction,…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
Nonlinear optics underpins quantum photonics by enabling the generation and control of quantum states of light. We present new applications of optical resonators as mode selectors in nonlinear processes. First, we show that cavity-enhanced…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
In the resonance model, high-frequency quasi-periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic continuum within the framework of the functional renormalization group. The formalism allows us to determine complete physical…
We explore the nonlinear dynamics of a cavity optomechanical system. Our realization consisting of a drumhead nano-electro-mechanical resonator (NEMS) coupled to a microwave cavity, allows for a nearly ideal platform to study the…
We give a detailed and improved presentation of our recently proposed formalism for non-linear perturbations in cosmology, based on a covariant and fully non-perturbative approach. We work, in particular, with a covector combining the…
Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
An exact solution to the interaction between two emitters mediated by F\"{o}rster resonance energy transfer is presented. The system is comprised of a one-dimensional optical waveguide with two embedded two-level systems and is analyzed…
One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a…