Related papers: Oscillation and synchronization of two quantum van…
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral…
We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest…
In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an…
Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by low number of excitations and a highly non-classical steady state of the self-sustained oscillator. Several existing proposals of observing…
Classical and quantum anharmonic noncommutative oscillators with quartic self-interacting potential are considered and the effect of self-interaction term on the free energy and partition function of both models is calculated to first order…
The behavior of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimera-like regimes are observed at small values of the coupling strength parameter. Synchronization takes…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
Quantization of the damped harmonic oscillator is taken as leitmotiv to gently introduce elements of quantum probability theory for physicists. To this end, we take (graduate) students in physics as entry level and explain the physical…
The classical boundaries of the quantum singular oscillator (SO) is addressed under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to comparatively evaluate phase-space and configuration space quantum trajectories as well as to…
Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it difference} operator. Meixner oscillators include as limits…
Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories . Not so with the eigenvalues ($\pm 1$) of the parity…
We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…