Related papers: Stability of long-sustained oscillations induced b…
We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
The voltage dependence of nanoelectromechanical effects in a system where the quantized mechanical vibrations of a quantum dot are coupled to coherent tunneling of electrons through a single level in the dot is studied. It is found that…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Research on the emergence of thermodynamics in closed quantum systems under unitary time evolution arrived at the consensus that generic systems equilibrate under rather general assumptions. A new focus of the field is thus on exceptions.…
We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality.…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…
Self-oscillators are intriguing due to their ability to sustain periodic motion without periodic stimulus. They remain rare as achieving such behavior requires a balance of energy input, dissipation and non-linear feedback mechanism. Here,…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…
A unified theory of the temporal current self-oscillations is presented. We establish these oscillations as the manifestations of limit cycles, around unstable steady-state solutions caused by the negative differential conductance. This…
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the…
Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus…
We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial…
The dynamic interplay of transport, electrostatic, and magnetic effects in the resonant tunneling through ferromagnetic quantum wells is theoretically investigated. It is shown that the carrier-mediated magnetic order in the ferromagnetic…
The possibility of the existence of natural self-oscillation of a free electron is suggested. This oscillation depends on the interaction of the electron with its own electromagnetic fields. Suitable standing wave solutions of the…
Understanding the non-deterministic behavior of deterministic nonlinear systems has been an implicit dream since Lorenz named it the "butterfly effect". A prominent example is the hysteresis and bistability of the Duffing oscillator, which…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…