The many-body problem
The long-lasting “many-body” quantum problem ……
It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem. Max Born, 1960
Quantum mechanics describe exotic properties of atomic or nanoscale systems, without classical counterparts. Thus, there is a great (theoretical and experimental) interest in understanding such properties in order to create new materials, electron devices, etc. However, from a computational point of view, the exact solution of quantum systems (i.e. solving the many-body Schrödinger equation) is only accessible for very few particles. This computational barrier is at the heart of almost all unsolved problems in Quantum mechanics and it explains why many atomic or nanoscale systems remain still unexplored.
Some of the most beautiful and elegant physical theories developed during last century tackle this “many-body” problem. In fact, most of these theories are developed for equilibrium states with weak correlations, which are certainly much easier to study than non-equilibrium states or strongly correlated systems. For example, Quantum Monte Carlo methods or the Density Functional Theory has been used worldwide to study (minimum energy) equilibrium systems. The former formalism was developed by Dr. J.Pople and the last was proposed by Dr. W. Kohn who, both, received the Nobel Prize in Chemistry in 1998 for "for his development of computational methods in quantum chemistry" and “for his development of the Density Functional Theory”, respectively. Much m ore work is still needed to correctly treat the “many-body” problem in strongly correlated system or in open systems far from equilibrium conditions (such as electron devices).
…. my original contribution to the long-lasting “many-body” problem
From a theoretical point of view, my main research activity is devoted to face this “many-body” problem using many-particle quantum (Bohm) trajectories. In particular, I demonstrate these quantum trajectories provide a privileged framework to take into account Coulomb and exchange correlations in time-dependent open (far from equilibrium) systems.
See practical applications for electronics in BITLLES_development