One-dimensional surface diffusion: Density dependence in a smooth potential

1997 ◽  
Vol 107 (10) ◽  
pp. 4015-4023 ◽  
Author(s):  
J. J. M. Beenakker ◽  
S. Yu. Krylov
Keyword(s):  
Density Dependence ◽  
Surface Diffusion ◽  
One Dimensional ◽  
Smooth Potential ◽  
Dimensional Surface

One dimensional surface diffusion. II. Density dependence in a corrugated potential

1997 ◽  
Vol 107 (17) ◽  
pp. 6970-6979 ◽  
Author(s):  
S. Yu. Krylov ◽  
A. V. Prosyanov ◽  
J. J. M. Beenakker
Keyword(s):  
Density Dependence ◽  
Surface Diffusion ◽  
One Dimensional ◽  
Dimensional Surface

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Fractal fits to Riemann zeros

2007 ◽  
Vol 85 (4) ◽  
pp. 345-357 ◽  
Author(s):  
P B Slater
Keyword(s):  
Potential Model ◽  
Sine Series ◽  
Dominant Term ◽  
One Dimensional ◽  
Smooth Potential ◽  
Smooth Part ◽  
Least Squares Fit ◽  
The One ◽  
Higher Order Corrections ◽  
03.65 Sq

Wu and Sprung (Phys. Rev. E, 48, 2595 (1993)) reproduced the first 500 nontrivial Riemann zeros, using a one-dimensional local potential model. They concluded — as did van Zyl and Hutchinson (Phys. Rev. E, 67, 066211 (2003)) — that the potential possesses a fractal structure of dimension d = 3/2. We model the nonsmooth fluctuating part of the potential by the alternating-sign sine series fractal of Berry and Lewis A(x,γ). Setting d = 3/2, we estimate the frequency parameter (γ), plus an overall scaling parameter (σ) that we introduce. We search for that pair of parameters (γ,σ) that minimizes the least-squares fit Sn(γ,σ) of the lowest n eigenvalues — obtained by solving the one-dimensional stationary (nonfractal) Schrodinger equation with the trial potential (smooth plus nonsmooth parts) — to the lowest n Riemann zeros for n = 25. For the additional cases, we study, n = 50 and 75, we simply set σ = 1. The fits obtained are compared to those found by using just the smooth part of the Wu–Sprung potential without any fractal supplementation. Some limited improvement — 5.7261 versus 6.392 07 (n = 25), 11.2672 versus 11.7002 (n = 50), and 16.3119 versus 16.6809 (n = 75) — is found in our (nonoptimized, computationally bound) search procedures. The improvements are relatively strong in the vicinities of γ = 3 and (its square) 9. Further, we extend the Wu-Sprung semiclassical framework to include higher order corrections from the Riemann–von Mangoldt formula (beyond the leading, dominant term) into the smooth potential. PACS Nos.: 02.10.De, 03.65.Sq, 05.45.Df, 05.45.Mt

Discrete one dimensional surface solitons

2007 ◽  
Author(s):  
G. Stegeman ◽  
D. Christodoulides ◽  
S. Suntsov ◽  
K. Makris ◽  
G. Siviloglou ◽  
...  
Keyword(s):  
One Dimensional ◽  
Dimensional Surface

scholarly journals Giant Rashba splitting of quasi-one-dimensional surface states on Bi/InAs(110)- (2×1)

2018 ◽  
Vol 98 (7) ◽  
Author(s):  
Takuto Nakamura ◽  
Yoshiyuki Ohtsubo ◽  
Yuki Yamashita ◽  
Shin-ichiro Ideta ◽  
Kiyohisa Tanaka ◽  
...  
Keyword(s):  
Surface States ◽  
One Dimensional ◽  
Dimensional Surface
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