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)