Peter Pan

McMahon, Lynne

doi:10.2307/25305829

Cited by 1 publication

(2 citation statements)

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“…(23) shows that R(x) is a Gaussian. The easiest way to compute R(x) as t → ∞ is to assume the simple saturation approximation (24). Replacing a i → sign(a i ), the autocorrelation at t → ∞ is found to be:…”

Section: Autocorrelation Functionmentioning

confidence: 99%

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Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators

Hamerly

Inagaki

Takesue

et al. 2016

Int. J. Mod. Phys. B

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A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this "Ising machine" for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear "growth stage" and a nonlinear "saturation stage". These predictions are compared against recent data for a 10,000-spin 1D Ising machine. arXiv:1605.08121v1 [physics.optics] 26 May 2016 J 1 =0.2,J 2 =0.3 J 1 =0.35,J 2 =0.15 J 1 =0.15,J 2 =0.35 0 50 100 150 J 1 =0.3,J 2 =0.2 50 100 150 Pulse i Topological defect formation in 1D and 2D spin chains realized by network of OPOs 21 J 1 =0.45,J 2 =0.05

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Section: Autocorrelation Functionmentioning

confidence: 99%

“…This suggests that the full numerical model works well, but Eq. (34), which relies on the simple saturation assumption (24), is inaccurate. This is the result of domain-wall motion and collision in the saturation stage, which reduces the number of defects as t → ∞.…”

Section: Defect Densitymentioning

confidence: 99%