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Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the…
The one-component $\lambda\phi^4$ theory in four dimensions in the spontaneously broken symmetry phase has a non-trivial, non-perturbative sector which can be studied by means of a duality transformation of its Ising limit. Duality maps…
We model backscatter for electric fields propagating through optical micro-ring resonators, as occurring both in-ring and in-coupler. These provide useful tools for modelling transmission and in-ring fields in these optical devices. We then…
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…
We experimentally demonstrate stimulated four-wave mixing in two linearly uncoupled integrated Si$_3$N$_4$ micro-resonators. In our structure the resonance combs of each resonator can be tuned independently, with the energy transfer from…
We construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the…
Combined spectrally and time resolved measurements provide information not otherwise available if performed in either domain alone. We demonstrate a new approach to Four Wave Mixing spectroscopy, where spectral selectivity is achieved by…
We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrodinger-type equations. For illustrative…
We study phase conjugation in a nonlinear composite slab when the counter propagating pump waves are completely absorbed by means of coherent perfect absorption. Under the undepleted pump approximation the coupling constant and the phase…
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum…
In general the ubiquitous \chi^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes…
We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems…
Proposing an optomechanical cavity modulated periodically, we study the modulation synchronization of mechanical modes of the mirrors. A periodic modulation is applied to one of the mirrors, where the second mirror has the capability of…
Consider the transverse magnetic polarization of the electromagnetic scattering of a plane wave by a perfectly conducting plane surface, which contains a two-dimensional subwavelength rectangular cavity. The enhancement is investigated…
We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $\theta$. Being to a large extent analytically solvable, the model reveals a rich $\theta$ dependence of the…
An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of…
Dynamics of two anharmonic oscillators with interaction of the fourth order has been investigated. The conditions at realization of which system is integrable are established. The exact analytical solution of the nonlinear equations in the…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we…
The extension of nonlinear spectroscopic techniques into the x-ray domain is in its infancy but holds the promise to provide unique insight into the dynamics of charges in photoexcited processes, which are of fundamental as well as applied…