Related papers: Integrable nonlinear parity-time symmetric optical…
The reliability of the approximations commonly adopted in the calculation of static optical (hyper)polarizabilities is tested against exact results obtained for an interesting toy-model. The model accounts for the principal features of…
In this work, we propose an all-optical stroboscopic scheme to simulate an open quantum system. By incorporating the tritter, consisting of a group of beam splitters, we find the emergence of spontaneous anti-phase synchronization in the…
We propose a grated microcavity setup to form trapped polariton condensates with parity-time ($\mathcal{PT}$) symmetry and study their polarization dynamics. The pseudo-conservative dynamics of the Stokes vector in proposed configuration is…
We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a…
The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges…
Open physical systems with balanced loss and gain, described by non-Hermitian parity-time ($\mathcal{PT}$) reflection symmetric Hamiltonians, exhibit a transition which could engenders modes that exponentially decay or grow with time and…
The Mott-insulating phase of the two-dimensional (2d) Bose-Hubbard model is expected to be characterized by a non-local brane parity order. Parity order captures the presence of microscopic particle-hole fluctuations and entanglement, whose…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
We study theoretically an optical cavity and a parity-time ($\mathcal{PT}$)-symmetric pair of mechanical resonators, where all oscillators are pairwise coupled, forming an optomechanical system with a closed-contour interaction. Due to the…
In the model system of two instantaneously and symmetrically coupled identical Stuart-Landau oscillators we demonstrate that there exist stable solutions with symmetry-broken amplitude- and phase-locking. These states are characterized by a…
We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an…
We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and…
We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
We show that parity-time and partial parity-time symmetries are particular cases of antiunitary symmetry. This point is illustrated by means of a recently discussed system of non-Hermitian coupled harmonic oscillators that also exhibits…
Using a discrete mode approach we investigate the intermodal dynamics in a frequency comb with nonlinear coupling due to four-wave mixing. In the presence of sufficient saturable absorption, phase space collapses into a single state, and…
We calculated the eigenvalues for a general N-channel coupled system with parity-time symmetry due to equal loss/gain. We found that the eigenspectrum displays a mixing of parity-time symmetric and broken phases, with N-2 of the eigenvalues…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed…