Related papers: Amplitude bounds for biochemical oscillators
We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in…
We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target…
The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an…
Optical oscillators present a powerful optimization mechanism. The inherent competition for the gain resources between possible modes of oscillation entails the prevalence of the most efficient single mode. We harness this 'ultrafast'…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
A theoretical framework is developed for a precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the…
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations…
It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length…
Collective oscillation of cells in a population has been reported under diverse biological contexts and with vastly different molecular constructs. Could there be common principles similar to those that govern spontaneous oscillation in…
This paper describes a new mechanism that might help with defining pattern sequences, by the fact that it can produce an upper bound on the ensemble value that can persistently oscillate with the actual values produced from each pattern.…
The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…
Real-world control applications in complex and uncertain environments require adaptability to handle model uncertainties and robustness against disturbances. This paper presents an online, output-feedback, critic-only, model-based…
Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with…
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…
Understanding the oscillating behaviors that govern organisms' internal biological processes requires interdisciplinary efforts combining both biological and computer experiments, as the latter can complement the former by simulating…
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by…