Numerical solutions for non-Markovian stochastic equations of motion

Farias, Ricardo L. S.; Ramos, Rudnei O.; Silva, L. A. da

doi:10.1016/j.cpc.2008.12.005

Cited by 21 publications

(18 citation statements)

References 12 publications

(13 reference statements)

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“…5(b)] evidences non-Markovian dynamics [56]. Non-Markovian dynamics are usually associated with noninstantaneous system-environment interactions (dissipation) and with colored noise in the driving force according to the fluctuation-dissipation relation [53,54,[57][58][59][60]. In contrast, we demonstrate non-Markovian dynamics emerging from noninstantaneous effective photon-photon interactions, which suppress fast switchings between metastable states regardless of the noise spectrum.…”

mentioning

confidence: 76%

Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity

et al. 2020

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We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent −1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.

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mentioning

confidence: 76%

Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity

et al. 2020

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“…In the present case, both the local damping and the Markovian nature of the noise follow from the BreitWigner approximation and the assumption of a thermal bath. Indeed the Breit-Wigner ansatz (61), see also (50) (41). In terms of the equivalent Langevin description, this corresponds to white noise.…”

Section: Markovian Langevin Dynamicsmentioning

confidence: 99%

“…Existing comparisons between given non-Markovian Langevin dynamics and their Markovian versions, see e.g. [48][49][50][51] indicate that, indeed, the better the separation of scales, i.e. the weaker the local damping, the better the Markovian approximation.…”

Section: Introductionmentioning

confidence: 99%

Langevin description of nonequilibrium quantum fields

Gautier

Serreau

2012

Phys. Rev. D

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We consider the non-equilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly non-local, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.

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“…Ref. [30]), like in a linear approximation to V eff (ϕ), usually valid only at short times. Complete solutions describing the evolution of the system to equilibrium can be obtained only through extensive numerical simulations.…”

Section: Lattice Renormalizationmentioning

confidence: 99%