Vitayard OCT.2013 | Page 9

http://vitayard.in Open Science and Research Project OKFN, India statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model. Cite as: arXiv:1308.0660 [cond-mat.stat-mech] (or arXiv:1308.0660v1 [cond-mat.stat-mech] for this version) Read full version at : Paper Schrödinger Equation on Fractals Curves Imbedding in $R^3$ Alireza Khalili Golmankhaneh, Ali Khalili Golmankhaneh, Dumitru Baleanu Description: In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been suggested on fractal curve. Using $F^{\alpha}$-calculus and Feynman path method we found the Schr\”{e}dinger on fractal timespace. The Hamiltonian operator and momentum operator has been derived. More, the continuity equation and the probability density is given in generalized formulation. Cite as: Read full version at : Paper 9 arXiv:1308.0291 [math-ph] (or arXiv:1308.0291v1 [math-ph] for this version)