scholarly journals Dean-Kawasaki dynamics: ill-posedness vs. triviality

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Vitalii Konarovskyi ◽  
Tobias Lehmann ◽  
Max-K. von Renesse
Keyword(s):  
Kawasaki Dynamics

scholarly journals Fluctuations for Kawasaki Dynamics

2005 ◽  
Vol 119 (3-4) ◽  
pp. 827-852 ◽  
Author(s):  
Cèdric Bernardin
Keyword(s):  
Kawasaki Dynamics

Generalized Kawasaki dynamics of the Heisenberg model

1995 ◽  
Vol 51 (5) ◽  
pp. 4155-4158 ◽  
Author(s):  
Zhengping Zhang
Keyword(s):  
Heisenberg Model ◽  
Kawasaki Dynamics

scholarly journals EQUILIBRIUM KAWASAKI DYNAMICS OF CONTINUOUS PARTICLE SYSTEMS

2007 ◽  
Vol 10 (02) ◽  
pp. 185-209 ◽  
Author(s):  
YURI KONDRATIEV ◽  
EUGENE LYTVYNOV ◽  
MICHAEL RÖCKNER
Keyword(s):  
Stochastic Dynamics ◽  
A Priori ◽  
Scaling Limit ◽  
Glauber Dynamics ◽  
Particle Systems ◽  
Death Process ◽  
Kawasaki Dynamics ◽  
Interacting Particles ◽  
Lattice Spin Systems ◽  
Diffusion Dynamics

We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the a priori explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).

scholarly journals Droplet growth for three-dimensional Kawasaki dynamics

2003 ◽  
Vol 125 (2) ◽  
pp. 153-194 ◽  
Author(s):  
F. den Hollander ◽  
F.R. Nardi ◽  
E. Olivieri ◽  
E. Scoppola
Keyword(s):  
Three Dimensional ◽  
Droplet Growth ◽  
Kawasaki Dynamics

DAMAGE SPREADING ON THE HOMO- AND HETERO-CELL LATTICES WITH COMPETING GLAUBER AND KAWASAKI DYNAMICS

2008 ◽  
Vol 22 (16) ◽  
pp. 2545-2555 ◽  
Author(s):  
Z. Z. GUO ◽  
XIAO-WEI WU
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Hexagonal Lattice ◽  
Interaction Strength ◽  
Spin Interaction ◽  
Kawasaki Dynamics ◽  
Range Interaction ◽  
Damage Spreading ◽  
Spin Interactions ◽  
Long Range Interaction

The damage spreading of the Ising model on the homo- and hetero-cell lattices (here the topological hexagonal lattice and the 4–8 lattice) with competing Glauber (G-) and Kawasaki (K-) dynamics is studied and the results are compared. For the homo-cell lattice, we pay attention to the pure K-dynamics or the cases in which the K-dynamics is dominant. We get four main conclusions related to the K-dynamics through our calculations: (1) the damage always spreads as long as Kawasaki dynamics is dominant during the competition of two dynamics; (2) the relation for the saturation damage, 〈s〉∞ = 0.5, holds for K-dynamics whatever the updating rules are; (3) 〈s〉∞ = 0.5 is independent of the structures of the system; (4) the DS process under pure K-dynamics converges very slowly, especially for T = 0 K-dynamics. For the hetero-cell lattice, we are interested in the long-range interaction between spins and the different interaction strength for the spins in the hetero-cells. To include the long-range spin interaction, we consider the spin interactions up to next-nearest neighbors. It is shown that the inclusion of the next-nearest-neighbor interaction enhances the transition temperature greatly. The explanation and discussion for the results are presented.

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