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Evolution equations for the moments of a photonic quantum state propagating through atmospheric turbulence are derived. These evolution equations are obtain from an evolution equation for the characteristic functional of the state,…
A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of…
Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on…
Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally/antinormally ordered moments of photon creation and annihilation operators. Extraction of these…