“The
underlying physical laws necessary for a large part of physics and the whole of chemistry
are thus completely known, and the difficulty is only that the exact
applications of these laws lead to equations much too complicated to be soluble.”
– Paul Dirac, 1929
As stated by Dirac, physical laws for atomic and molecular scale are well known. Schrödinger equation describes most of the strange phenomena such as entanglement occurring in quantum world for non-relativistic systems. However, solving this simple equation even for some small amount of fermions is still a challenging task for todays science. Problem arises because of the exponentially scaling phase space volume with increasing indistinguishable particle number. Even though, bosonic systems have also this problem of exponential scaling, solution can be found with good accuracy using quantum Monte Carlo methods. However, fermionic systems have the so called fermion sign problem arising from the antisymmetry condition of the wavefunction and therefore could not be solved so far without some sort of approximations.
All the matter we deal with in our daily lives have fermionic nature and therefore solution of Schrödinger equation for fermionic systems has great importance. My current thesis work is about development of new methodologies for Diffusion Monte Carlo concerning fermionic systems.
Recent Publications
Stability analysis of graphene nanoribbons by molecular dynamics simulations, N. Dugan, S. Erkoc, Phys. Stat. Sol. (b) 245, No. 4, 695 - 700 (2008) (PDF)
Genetic algorithm-Monte Carlo hybrid method for geometry optimization of atomic clusters, N Dugan, S. Erkoc, Computational Materials Science 45, 127(2009)
Genetic Algorithm Application to the Structural Properties of Si-Ge Mixed Clusters, N. Dugan, S. Erkoc, Materials and Manufacturing Processes 24, 250(2009)
Genetic Algorithms in Application to the Geometry Optimization of Nanoparticles, N. Dugan, S. Erkoc, Algorithms 2, 410(2009) (Open Access)
Given Talks and Posters
Shifted Wavefunction Diffusion Monte Carlo for Fermions (JPG)
Fermion Sign Problem in Diffusion Monte Carlo (PDF)
Quantum Monte Carlo methods for fermionic systems (PPT)
Linear scaling electronic structure methods (PPT)
Genetic Algorithm - Monte Carlo hybrid method for geometry optimization of atomic clusters (PPT)