Related papers: Dynamical symmetry breaking through AI: The dimer …
Classic control techniques typically rely on a model of the system's response to external inputs, which is difficult to obtain from first principles especially if the unknown dynamics are nonlinear. In this paper, we address this issue by…
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
We study the formation of stationary localized states using the discrete nonlinear Schr\"{o}dinger equation in a Cayley tree with connectivity $K$. Two cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear system are…
Trapped ions are an ideal platform to implement quantum simulation. Previously the parity-time reversal ($\mathcal{PT}$) symmetry-breaking transition in the paradigmatic non-Hermitian Hamiltonian $h_{PT}=J\sigma_x-i\Gamma\sigma_z$ has been…
The dynamics of open quantum systems is determined by avoided and true crossings of eigenvalue trajectories of a non-Hermitian Hamiltonian. The phases of the eigenfunctions are not rigid so that environmentally induced spectroscopic…
The paper discusses the basic paradoxes of thermodynamics and quantum mechanics. The approaches to solution of these paradoxes are suggested. The first one relies on the influence of the external observer (environment), which disrupts the…
We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and BEC (by means of an…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…
Many real-world systems are governed by the time-dependent, nonlinear differential equations. Dynamics of an electrical system are also best described using the very equations. Being one of the preferred machines when using advanced control…
A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be…
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
We investigate two key aspects of quantum systems by using the Tavis-Cummings dimer system as a platform. The first aspect involves unraveling the relationship between the phenomenon of self-trapping (or lack thereof) and integrability (or…
In recent years there have been significant advances in the study of many-body interactions between atoms and light confined to optical cavities. One model which has received widespread attention of late is the Dicke model, which under…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…
We systematically characterize the dynamical evolution of time-parity (PT )-symmetric two-level systems with spin-dependent dissipations. If the control parameters of the gap are linearly tuned with time, the dynamical evolution can be…
We propose a novel framework to analyze symmetry breaking in dynamical systems through the lens of entropy and information transfer. Information transfer quantifies the directional exchange of entropy between observables, allowing us to…