scholarly journals Small noise and long time phase diffusion in stochastic limit cycle oscillators

2018 ◽  
Vol 264 (2) ◽  
pp. 1019-1049 ◽  
Author(s):  
Giambattista Giacomin ◽  
Christophe Poquet ◽  
Assaf Shapira
Keyword(s):  
Limit Cycle ◽  
Small Noise ◽  
Phase Diffusion ◽  
Stochastic Limit ◽  
Long Time

scholarly journals A Variational Method for Analyzing Stochastic Limit Cycle Oscillators

2018 ◽  
Vol 17 (3) ◽  
pp. 2205-2233 ◽  
Author(s):  
Paul C. Bressloff ◽  
James N. MacLaurin
Keyword(s):  
Variational Method ◽  
Limit Cycle ◽  
Stochastic Limit

scholarly journals Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 200 ◽  
Author(s):  
Andy Chia ◽  
Michal Hajdušek ◽  
Rosario Fazio ◽  
Leong-Chuan Kwek ◽  
Vlatko Vedral
Keyword(s):  
Signal To Noise Ratio ◽  
Noise Analysis ◽  
Photon Number ◽  
Optical Field ◽  
Signal To Noise ◽  
Small Noise ◽  
Phase Diffusion ◽  
Small Noise Approximation ◽  
Linear Amplifier ◽  
Phase Uncertainty

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.

scholarly journals Synchronization of coupled stochastic limit cycle oscillators

2010 ◽  
Vol 374 (15-16) ◽  
pp. 1712-1720 ◽  
Author(s):  
Georgi S. Medvedev
Keyword(s):  
Limit Cycle ◽  
Stochastic Limit

Entropy production and fluctuation theorem along a stochastic limit cycle

2008 ◽  
Vol 129 (11) ◽  
pp. 114506 ◽  
Author(s):  
Tie Jun Xiao ◽  
Zhonghuai Hou ◽  
Houwen Xin
Keyword(s):  
Entropy Production ◽  
Limit Cycle ◽  
Fluctuation Theorem ◽  
Stochastic Limit

Nonequilibrium Thermodynamic State Variables of Human Self-Paced Rhythmic Motions: Canonical-Dissipative Approach, Augmented Langevin Equation, and Entropy Maximization

2015 ◽  
Vol 22 (01) ◽  
pp. 1550007 ◽  
Author(s):  
S. Kim ◽  
J. M. Gordon ◽  
T. D. Frank
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Limit Cycle ◽  
Langevin Equation ◽  
Oscillation Frequency ◽  
Nonequilibrium Thermodynamic ◽  
State Variables ◽  
Thermodynamic State ◽  
Stochastic Limit ◽  
Limit Cycle Oscillator

Nonequilibrium thermodynamic state variables are derived for a stochastic limit-cycle oscillator model that has been used in motor control research to describe human rhythmic limb movements. The nonequilibrium thermodynamic state variables are regarded as counterparts to the thermodynamic state variables entropy, internal energy, and free energy of equilibrium systems. The derivation of the state variables is based on maximum entropy distributions of the Hamiltonian energy of the stochastic limit-cycle oscillators. The limit-cycle oscillator model belongs to the class of canonical-dissipative systems, on the one hand, and, on the other hand, can be cast into the form of an augmented Langevin equation. Both concepts are known as physical models for open systems. Experimental data from paced and self-paced pendulum swinging experiments are presented and estimates for the nonequilibrium thermodynamic state variables are given. Entropy and internal energy increased with increasing oscillation frequency both for the paced and self-paced conditions. Interestingly, the nonequilibrium free energy decayed when oscillation frequency was increased, which is akin to the decay of the Landau free energy when the control parameter is scaled further away from its critical value.

Long time, large scale properties of the noisy driven-diffusion equation

1994 ◽  
Vol 446 (1926) ◽  
pp. 67-85 ◽  
Keyword(s):  
Diffusion Equation ◽  
Large Scale ◽  
Noise Spectrum ◽  
Dynamical Equations ◽  
Scaling Exponents ◽  
Small Noise ◽  
Nonlinear Dynamical ◽  
Theoretical Approaches ◽  
Long Time ◽  
Scale Properties

We study the driven-diffusion equation, describing the dynamics of density fluc­tuations δρ(x → , t) in powders or traffic flows. We have performed quite detailed numerical simulations of this equation in one dimension, focusing in particular on the scaling behaviour of the correlation function <δρ(x → , t)δρ(0, 0)> . One of our motivations was to assess the validity of various theoretical approaches, such as Renormalization Group and different self consistent truncation schemes, to these nonlinear dynamical equations. Although all of them are seen to predict correctly the scaling exponents, only one of them (where the non-exponential nature of the relaxation is taken into account) is able to reproduce satisfactorily the value of the numerical prefactors. Several other interesting issues, such as the noise spectrum of the output current, or the statistics of distance between jams (showing a transition between a ‘laminar’ régime for small noise to a ‘jammed’ régime for higher noise) are also investigated.

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