Related papers: Computing with Dynamical Systems Based on Insulato…
The desire to exert active optical control over matter is a unifying theme across multiple scientific disciplines, as exemplified by all-optical magnetic switching, light-induced metastable or exotic phases of solids and the coherent…
In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the…
Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…
We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which…
Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady…
An optomechanical oscillator undergoes a Hopf bifurcation that connects two dynamical regimes with different information-processing capabilities: thermal Brownian motion and coherent self-sustained oscillation. Below threshold, the…
We have varied the disorder in a two-dimensional electron system in silicon by applying substrate bias. When the disorder becomes sufficiently low, we observe the emergence of the metallic phase, and find evidence for a metal-insulator…
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and…
We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…
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…
It is an intriguing concept to use oscillators as fundamental building blocks of electronic computers. The idea is not new, but is currently subject to intense research as a part of the quest for 'beyond Moore' electronic devices. In this…
Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry.…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
With this work we present two new methods for the generation of thermostated, manifestly Hamiltonian dynamics and provide corresponding illustrations. The basis for this new class of thermostats are the peculiar thermodynamics as exhibited…
In a recent experiment, Barreiro et al. demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions [Nature 470, 486 (2011)]. Using up to five ions, single- and multi-qubit entangling gate operations…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms,…
We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase which is stabilized by electronic interactions, from the insulating phase where…
We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable to show complex hysteresis. The system is a…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…