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The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
We investigate the dynamical properties of the XY spin 1/2 chain with infinite-range transverse interactions and find a dynamical phase transition with a chaotic dynamical phase. In the latter, we find non-vanishing finite-time Lyapunov…
It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighbourhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states,…
We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear…
We investigate several dynamical regimes characterizing a bosonic binary mixture loaded in a ring trimer, with particular reference to the persistence of demixing. The degree of phase separation is evaluated by means of the "Entropy of…
A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired…
We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems…
By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Preparation of pure states on networks of quantum systems by controlled dissipative dynamics offers important advantages with respect to circuit-based schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are considered,…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…