Density Functional Theory-Based Quantum Mechanics/Coarse-Grained Molecular Mechanics: Theory and Implementation

Density functional theory and quantum computation

Frank Gaitan1,2,3 and Franco Nori1,3,4 1Advanced Science Institute, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan 2Department of Physics, Southern Illinois University, Carbondale, Illinois 62901-4401, USA 3CREST, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan 4Department of Physics, Center for Theoretical Physics, Unive...

Quantum Hydrodynamic Model of Density Functional Theory

In this paper, we extend the method in [5] to derive a class of quantum hydrodynamic models for the density-functional theory (DFT). The most popular implement of DFT is the Kohn-Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn-Sham equation is a non-linear Schrödinger equation, and the corresponding Wigner equati...

Quantum Mechanics and Group Theory

where xi is the the Cartesian coordinate of a point particle of mass m, Fi is the external force applied to the particle, and the force is assumed to be conservative, the negative gradient of a potential energy function V (x). Newtonian mechanics for rigid bodies can be formulated in a similar way, and this approach can even be extended to relativistic point mechanics. The calculus of variation...

Functional methods underlying classical mechanics, relativity and quantum theory

The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is ”made” of these functions and becomes a submanifold in a Hilbert space of states of the particle. The...

Localized-density-matrix implementation of time-dependent density-functional theory