Related papers: Quantum Chaos as an Essential Resource for Full Qu…
Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
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,…
A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax towards an equilibrium. It is found…
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hbar$ is increased. We show evidence to the contrary in the behavior of…
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…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
Achieving full control of the time-evolution of a many-body quantum system is currently a major goal in physics. In this work we investigate the different ways in which the controllability of a quantum system can be influenced by its…
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of…
We study the quantum dynamics generated by the repeated action of a non-unitary evolution operator on a system of qubits. Breaking unitarity can lead to the purification of mixed initial states, which corresponds to the loss of sensitivity…
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we…
We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute…
A new model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse to a classical state is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase.…
We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic…
This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…