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CONTINUUM RELAXATION OF INTERACTING STEPS ON CRYSTAL SURFACES IN 2+1 DIMENSIONS
crystal surface epitaxial growth morphological evolution Burton–Cabrera–Frank model Ehrlich–Schwoebel barrier entropic interactions elastic dipole interactions step chemical potential continuum limit surface mobility
2015/10/16
We study the relaxation of crystal surfaces in 2+1 dimensions via the motion ofinteracting atomic steps. The goal is the rigorous derivation of the continuum limit. The starting point is a discrete sc...
A stochastic step flow model with growth in 1+1 dimensions
stochastic step flow model growth 1+1 dimensions
2015/10/16
Mathematical implications of adding Gaussian white noise to the Burton– Cabrera–Frank model for N terraces (‘gaps’) on a crystal surface are studied under external material deposition for large N. The...
Homogenization of composite vicinal surfaces: Evolution laws in 1+1 dimensions
Crystal surface Burton–Cabrera–Frank (BCF) model Line defects Diffusion Macroscopic limit Multiscale expansion
2015/10/16
We apply classical homogenization to derive macroscopic relaxation laws for crystal surfaces with distinct inhomogeneities at the microscale. The proposed method relies on a formal multiscale expansio...
Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions
Actions Hierarchy of Attractive Nonlinear Oscillators the Quartic Oscillator 1+1 Dimensions Mathematical Physics
2012/4/23
In this paper, we present an explicit form in terms of end-point data for the classical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobi equation for each member of a hierarchy of...
Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions
Lie-algebraic interpretation the Coulomb-Rosochatius n dimensions Mathematical Physics
2011/9/20
Abstract: The potential group method is applied to the n-dimensional Coulomb-Rosochatius potential, whose bound states and scattering states are worked out in detail. As far as scattering is concerned...
Scaling and universality in two dimensions: three-body bound states with short-ranged interactions
two dimensions three-body bound states short-ranged interactions Quantum Gases
2011/10/8
Abstract: The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a ...
One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions
One-loop Renormalized Coefficient Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories
2011/7/28
Abstract: Recent studies of the $AdS_4/CFT_3$ correspondence involve the construction of a peculiar supersymmetric gauge theory on the worldvolume of multiple M2s branes as a boundary field theory. Un...
Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition
Eigenvalue Problem Two Dimensions Irregular Boundary II Neumann Condition
2011/7/26
Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition.
Anderson-like Transition for a Class of Random Sparse Models in d{leg}2 Dimensions
Random Sparse Models Anderson-like Transition Functional Analysis
2011/7/26
Abstract: We show that the Kronecker sum of d{\leg}2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around...
Comment on "A new exactly solvable quantum model in $N$ dimensions" [Phys. Lett. A 375(2011)1431, arXiv:1007.1335]
Position-dependent mass Arbitrary dimension N Solvable quantum model
2011/7/28
Abstract: We pinpoint that the work about "a new exactly solvable quantum model in $N$ dimensions" by Ballesteros et al. [Phys. Lett. A {\bf 375} (2011) 1431, arXiv:1007.1335] is not a new exactly sol...
Endpoint distribution of directed polymers in 1+1 dimensions
directed polymers Endpoint distribution Probability
2011/7/28
Abstract: We give an explicit formula for the joint density of the max and argmax of the Airy$_2$ process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint ...
We demonstrate that it is possible to determine the coecients of an all-order beta function linear in the anomalous dimensions using as data the two-loop coecients together with the first one of the...
Entropy Production in Gluodynamics in temporal axial gauge in 2+1 dimensions
Entropy Production Gluodynamics temporal axial gauge 2+1 dimensions
2011/1/7
Entropy production in non-Abelian gauge theory is discussed in the limit of vanishing classical fields. Based on the Kadanoff-Baym equation with the leading order self-energy in
the temporal axial ga...
Any l-state solutions of the Woods-Saxon potential in arbitrary dimensions within the new improved quantization rule
Woods-Saxon potential improved quantization rule Pekeris approximation
2010/10/27
The approximated energy eigenvalues and the corresponding eigenfunctions of the spherical
Woods-Saxon effective potential in D dimensions are obtained within the new improved quantization rule for al...
Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a mo...