Related papers: Symmetric States Requiring System Asymmetry
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
Spontaneous symmetry breaking is an essential feature of modern science. We demonstrate that it also plays an important role in the physics of complex plasmas. Complex plasmas can serve as a powerful tool for observing and studying discrete…
If a system undergoes symmetric dynamics, then the final state of the system can only break the symmetry in ways in which it was broken by the initial state, and its measure of asymmetry can be no greater than that of the initial state. It…
Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories,…
Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of…
Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an…
We study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…
We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…
The phenomenon of PT (parity- and time-reversal) symmetry breaking is conventionally associated with a change in the complex mode spectrum of a non-Hermitian system that marks a transition from a purely oscillatory to an exponentially…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially…
The phenomenon of spontaneous symmetry breaking is investigated in the dynamic thermalization of a degenerate quantum system. A three-level system interacting with a heat bath is carefully studied to this end. It is shown that the…