Related papers: Phase-locking in dynamical systems and quantum mec…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
Nonequilibrium dynamics are studied near the quantum phase transition point in the one-dimensional quantum Blume-Emery-Griffiths model. Its pseudo-spin component $ S^z $ represents an electric polarization, and $ (S^z)^2 $ corresponds to…
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light…
Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies $\omega_1$ and $\omega_2=r \omega_1$. We show that such drives may be used to tune towards dynamics induced…
Quantum Hall bilayers are a uniquely tunable platform that can realize continuous transitions between distinct topological phases of matter. One prominent example is the transition between the Halperin state and the Moore--Read Pfaffian,…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
Several mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of…
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase reduction theory recently developed for quantum nonlinear…
We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and…
Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian, $H^{W}(q,\,p)$, constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition are analytically obtained in terms of Wigner…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling…
In order to model the processes taking place in systems with Josephson contacts, a differential equation on a torus with three parameters is used. One of the parameters of the system can be considered small and the methods of the fast--slow…
We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that…
We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small…
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\"{o}dinger equation.…
In this work, we explore the dynamics of quantum correlations, namely coherence, entanglement, and nonlocality associated with a Bell state, in a dimeric arrangement of organic PBI molecules, mediated by dipole-dipole interactions, under…