Smoothening of a random surface as it results from the edwards-wilkinson kinetic equation |
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Authors: | Viktor Bezák |
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Institution: | (1) Department of Solid State Physics, Faculty of Mathematics and Physics, Comenius University, 842 15 Bratislava, Slovakia |
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Abstract: | The time evolution of a random surfacez=h(r, t) (r=x, y) formed by a deposition process of the Edwards-Wilkinson type is discussed. The discussion is based on the author’s former
derivation of the autocorrelation functionA
h(|r − r′|,t, t′)=〈h(r,t)h(r′,t′)〉 of the height functionh(r,t) under the assumption of a stochastic initial condition V. Bezák: Acta Physica Univ. Comenianae39 (1998) 135]. Under the assumption of a steady (non-zero) deposition rate, the varianceσ
h
2
(t)=〈h(r,t)]2〉 increases logarithmically in time whilst the correlation lengthl
h(t) of the height functionh(r,t) increases as ∼t
1/2. Therefore, the ratioσ
h(t)/l
h
(t) tends to zero and the surfacez=h(r,t) does always tend towards a smoothened appearance.
This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97. |
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Keywords: | |
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