Related papers: Megastable quantization in generalized pilot-wave …
We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, \emph{i.e.} megastability. In the low-memory regime, the equation reduces to a self-excited…
We show that work done by the non conservative forces along a stable limit cycle attractor of a dissipative dynamical system is always equal to zero. Thus, mechanical energy is preserved on average along periodic orbits. This balance…
We simulate the transformation of a classical fluid into a quantum-like (super)-fluid by the application of a generalized quantum potential through a retro-active loop. This numerical experiment is exemplified in the case of a non-spreading…
We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear…
Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Classical optomechanical systems feature self-sustained oscillations, where multiple periodic orbits at different amplitudes coexist. We study how this multistability is realized in the quantum regime, where new dynamical patterns appear…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
Non-normalizable states are difficult to interpret in the orthodox quantum formalism but often occur as solutions to physical constraints in quantum gravity. We argue that pilot-wave theory gives a straightforward physical interpretation of…
We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an…
A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave-particle duality at quantum scale where the wave is probabilistic by…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
We study evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…
Polarizable particles trapped in a resonator-sustained optical-lattice potential generate strong position-dependent backaction on the intracavity field. In the quantum regime particles in different energy bands are connected to different…
Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…