TY - JOUR
T1 - Second harmonic generation as a minimal model of turbulence
AU - Vladimirova, N
AU - Shavit, M
AU - Belan, S
AU - Falkovich, G
PY - 2021/7/22
Y1 - 2021/7/22
N2 - When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering a noise-driven system, we show that when one mode is pumped and another dissipates, the statistics of such cascades is never close to Gaussian, no matter what is the relation between interaction and noise. One finds substantial phase correlation in the limit of strong interaction or weak noise. Surprisingly, the mutual information between modes increases and entropy decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information, or entropy deficit, is encoded, and how singular measures form. For an instability-driven system, such as laser, even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from the equilibrium the conversion into the second harmonic is weakly affected by noise.
AB - When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering a noise-driven system, we show that when one mode is pumped and another dissipates, the statistics of such cascades is never close to Gaussian, no matter what is the relation between interaction and noise. One finds substantial phase correlation in the limit of strong interaction or weak noise. Surprisingly, the mutual information between modes increases and entropy decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information, or entropy deficit, is encoded, and how singular measures form. For an instability-driven system, such as laser, even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from the equilibrium the conversion into the second harmonic is weakly affected by noise.
UR - http://www.scopus.com/inward/record.url?scp=85110405200&partnerID=8YFLogxK
U2 - https://doi.org/10.1103/PhysRevE.104.014129
DO - https://doi.org/10.1103/PhysRevE.104.014129
M3 - مقالة
SN - 2470-0045
VL - 104
SP - 14129
EP - 14129
JO - Physical Review. E
JF - Physical Review. E
IS - 1
M1 - 014129
ER -