Related papers: Dynamical symmetry breaking through AI: The dimer …
In the present work we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schr\"odinger chain example, we present rigorous arguments that establish necessary…
We investigate semiclassical dynamics of a coupled atom-photon interacting system described by a dimer of anisotropic Dicke model in the presence of photon loss, exhibiting a rich variety of non-linear dynamics. Based on symmetries and…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in…
We study the interplay between nonlinearity in exciton transport and trapping due to a sink site for the dimer and the trimer with chain configuration by a numerical integration of the discrete nonlinear Schroedinger equation. Our results…
We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
We study the robustness of the selftrapping phenomenon exhibited by the Discrete Nonlinear Schrodinger (DNLS) equation against the effects of nonadiabaticity and quantum fluctuations in a two-site system (dimer). To test for nonadiabatic…
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…
This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…
We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites…
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and…
We extend our analysis of the effects of the interplay of quantum phases and nonlinearity to address saturation effects in small quantum systems. We find that initial phases dramatically control the dependence of self-trapping on initial…
We introduce \textbf{Schr\"{o}dinger AI}, a unified machine learning framework inspired by quantum mechanics. The system is defined by three tightly coupled components: (1) a {time-independent wave-energy solver} that treats perception and…
We propose a one-dimensional nonlinear system of coupled anharmonic oscillators that dynamically undergoes a topological transition switching from the {disordered} and topologically trivial phase into the nontrivial one due to the…
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
We consider dynamics of classical dimer models undergoing a phase transition to an ordered, frozen state. Relaxation processes are dominated by traps which are entropic in origin and can be traced to the locally jammed nature of the dimer…
We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is…