Related papers: Algebraic Theory of Quantum Synchronization and Li…
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Synchronization of quantum nonlinear oscillators has attracted much attention recently. To characterize the quantum oscillatory dynamics, we recently proposed a fully quantum-mechanical definition of the asymptotic phase, which is a key…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
Synchronization is a widespread phenomenon in science and technology. We here study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the…
Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review…
The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
We study synchronization in a two-node network built out of the smallest possible self-sustained oscillator: a spin 1. We first demonstrate that phase locking between the quantum oscillators can be achieved, even for limit cycles that…
We introduce logical synchrony, a framework that allows distributed computing to be coordinated as tightly as in synchronous systems without the distribution of a global clock or any reference to universal time. We develop a model of events…
A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…