Related papers: Rotating wave approximation: systematic expansion …
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
We report the first observation of Rabi oscillations in the spin-7/2 ensemble of trivalent gadolinium ions hosted in CaWO$_4$ single crystal. A number of transitions within the lowest electronic multiplet $^8S_{7/2}$ of Gd$^{3+}$ ion are…
Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final…
The Rabi Hamiltonian is studied in the dispersive regime and ultra-strong coupling. We employ a recent unitary transformation to obtain not only the approximate Hamiltonian and its energy levels but also its eigenfunctions. The relationship…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
A tractable N-state Rabi Hamiltonian is introduced by extending the parity symmetry of the two-state model. The single-mode case provides a few-parameter description of a novel class of periodic systems, predicting that the ground state of…
The 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use of the so-called space-time rays, which…
We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and…
Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems -- crucial for quantum technologies -- remains less understood. We develop a systematic toolbox…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…
We show that the correlation and entanglement dynamics of spin systems can be understood in terms of propagation of spin waves. This gives a simple, physical explanation of the behaviour seen in a number of recent works, in which a…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
A recent proposal for practical calculation of vibrational mode lifetimes is tested on simple, low-dimensional anharmonic models. The proposed scheme approximates the mode lifetime in terms of ensemble averages of specific functions in…
Spin-orbit coupling is widespread in binary asteroid systems and it has been widely studied for the case of ellipsoidal secondary. Due to angular momentum exchange, dynamical coupling is stronger when the orbital and rotational angular…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
Reliable low-latency gravitational wave parameter estimation is essential to target limited electromagnetic followup facilities toward astrophysically interesting and electromagnetically relevant sources of gravitational waves. In this…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in…
We provide an analysis of the correlation properties of spin and fermionic systems on a lattice evolving according to open system dynamics generated by a local primitive Liouvillian. We show that if the Liouvillian has a spectral gap which…