Quantum theory and high-fidelity mathematical models of DNA

This paper researches the mathematical modeling problem for DNA utilizing the quantum mechanics and Hamiltonian concept. We derived the Hamiltonian in order to find the equation of motion for complex DNA. This high-fidelity mathematical model allows one to study complex electronic and electro-mechanical phenomena in DNA. The importance of results is due to the fact that the proposed quasi three-dimensional (q3D) concept allows one to examine electronic and mechanical properties for DNA with thousands of base pairs. The density of states and the Lyapunov exponents for the wave function are derived. Folding, charge transport and other complex effects can be examined using the equations of motion derived. Finally, examples are reported.