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A dynamical algebra ${\cal A}_q$, englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the…
We consider the ground state of simple quantum systems coupled to an environment. In general the system is entangled with its environment. As a consequence, even at zero temperature, the energy of the system is not sharp: a projective…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
We study coherent oscillations in double quantum dots tunnel-coupled to metallic leads by means of full counting statistics of electron transport. If two such systems are coupled by Coulomb interaction, there are in total six (instead of…
We investigate a system of two coupled harmonic oscillators on the non-commutative plane \RR^2_{\theta} by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e.…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
When the coupling rate between two quantum systems becomes as large as their characteristic frequencies, it induces dramatic effects on their dynamics and even on the nature of their ground state. The case of a qubit coupled to a harmonic…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…
Decoherence for a one-dimensional coupled-resonator waveguide with a two-level system inside one of resonators, induced by their interaction with corresponding environments, is investigated. Each environment is modeled as a continuum of…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…
We study systems of a few charged bosons contained within a strongly anisotropic harmonic trap. A detailed examination of the ground-state correlation properties of two-, three-, and four-particle systems is carried out within the framework…
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of…