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Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions…
In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
With extensive variational simulations, dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied in a dense limit of environmental modes. By employing a generalized trial wave function composed of…
This paper studies the effect of perturbations on the gradient flow of a general nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable…
Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as a promising platform for artificial neuron design. In this work, we introduce a modeling and analysis…
Out-of-time-ordered-correlators (OTOCs) have been suggested as a means to diagnose chaotic behavior in quantum mechanical systems. Recently, it was found that OTOCs display exponential growth for the inverted quantum harmonic oscillator,…
We study the flow of energy between a harmonic oscillator (HO) and an external environment consisting of N two-degrees of freedom non-linear oscillators, ranging from integrable to chaotic according to a control parameter. The coupling…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
We present a general framework for incorporating non-reciprocal interactions into the Ising model with Glauber dynamics, without requiring multiple species. We then focus on a model with vision-cone type interactions. We solve it in a fully…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors.…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…