1. Department of Physics, Kyung Hee University
제13차 열 및 통계물리 워크샵
Drift와 결함이 있는 계의 표면 거칠기
Sooyeon Yoon & Yup Kim
Department of Physics, Kyung Hee University

2. Background of this study
• Edward-Wilkinson Eq.
• G. Pruessner (PRL 92, (2004))
v : drift velocity
with Fixed Boundary Condition (FBC)
 Surface roughness
L : system size
h : the height of surface
 Family-Vicsek Scaling behavior
EW universality class
Anomalous exponents

3. Motivation
1. What is the simple stochastic discrete surface growth model to
describe the EW equaiton with drift and FBC ?
• Numerical Integration
• Toy models : Family model,
Equilibrium Restricted Solid-On-Solid (RSOS) model …
 Stochastic analysis for the Langevin equation
( S.Y. Yoon & Yup Kim, JKPS 44, 538 (2004) )
2. Application
The effect of the defect and drift for the surface growth ?

4. A stochastic analysis of continuum Langevin equation
for surface growths
S.Y. Yoon & Yup Kim, JKPS 44, 538 (2004))
• Continuum Langevin Equation :
• Fokker-Planck Equation :
is the transition rate from H′ to H.
• Master Equation :
If we consider the deposition(evaporation) of only one particle at the unit evolution step.
( a is the lattice constant. )
(deposition)
(evaporation)

5. Model
• Evolution rate on the site
For the Edward-Wilkinson equation with drift,
• Determine the evolution of the center point (x0=L/2) by the defect strength.
x0=L/2
p x d (e )
d (e ) or

6. Simulation Results  Scaling Properties of the Surface Width
(FBC, p=0)
(PBC, p=1)

7.  Analysis of the Interface Profile~

8. Crossover (EWanomalous roughening) according to the defect strength

10. Phase transition of RSOS model with a defect site
: H.S.Song & J.M.Kim (Sae Mulli, 50, 221 (2005))
r : the distance from the center point
P : defect strength
P=0, facet Pc
P=1, RSOS EW
p=0
p=1

11. G  Application of the surface growth by the defect (Queuing problem). .
( a : lattice constant ) .
(  : particle density )
  G
slowly go out !
fast get in !

12. EW (p0)  Anomalous roughening (p=0)
Conclusion
We studied the phase transition of the stochastic model which
satisfies the Edward-Wilkinson equation with a drift and a defect
on the 1-dimensional system.
1. The scaling exponents are changed by the drift and the perfect defect.
Anomalous exponents
2. Crossover
EW (p0)  Anomalous roughening (p=0)
3. Application to the queuing phenomena ( at p=0 : perfect defect ).