Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation

The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

“…This indicates that their dynamics may be described by a linear Langevin equation as in ( 64). An analogous conclusion has been drawn for a slightly different setting in [45]. Using (62) and (63), we give an explicit approximation for the two-point correlation u(q, ω)u(q , ω ) ,…”

“…Up to a constant numerical prefactor, λ(0) equals λ eff from (3). At this point we adopt a DRG scheme introduced in [41,42] and analyzed in [43], which has been recently applied in [44,45]. It implies that the next step of the scheme consists in solving (55) and (56) for ν and 0 explicitly, making their scale dependence transparent.…”

“…As a last step we make the common identification |q| = 0 e −l (see e.g. [35,[39][40][41][42]44,45]) and obtain asymptotically for large values of l (i.e. |q| 1)…”

Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation

“…The above condition (20) is the content of the 3/2-rule by Orszag [35,46,47]. It is used in spectral codes, as the so-called dealiasing procedure (see, e.g., [35]).…”

“…An overview of the progress made can be found in, e.g., [9][10][11][12]. Regarding more recent theoretical developments on the aspect of the KPZ probability density functions and their respective universality classes we mention, e.g., [13][14][15][16][17][18][19][20]. Another active area of theoretical work deals with different types of correlated noise, see, e.g., [18,[21][22][23].…”