Related papers: Driven generalized quantum Rayleigh-van der Pol os…
Synchronization of self-sustained oscillators under fixed-frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow, deterministic…
We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…
We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…
We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -- (Q)ISSs -- which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We…
The ability to produce nonclassical wave in a system is essential for advances in quantum communication and computation. Here, we propose a scheme to generate highly nonclassical phonon emission statistics -- antibunched wave in a quantum…
Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol…
We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the…
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…
The synchronization of coupled organ pipes represents a nonlinear phenomenon. The investigation of synchronization effects in organ pipes using a model of time-delayed coupled Van der Pol oscillators shows that synchronization improves…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
In this paper, we study the dissipative dynamics of the Jaynes-Cummings model with phase damping in the presence of a classical homogeneous gravitational field. The model consists of a moving two-level atom simultaneously exposed to the…
We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but…
We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the…
A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…
Quantum synchronization has been a subject of intensive research in the last decade. In this work, we propose a quantum Li\'enard system whose classical equivalent features two limit cycles to one of which the system will converge. In the…
I argue that a single driven quantum Van der Pol oscillator should not be considered a dissipative time crystal, contrary to previous claims. In particular, I show that its phase is prone to randomly drift when considering dephasing or…
We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehat\sigma_z$. This type of systems…
The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving…
Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…
Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond…