Many-particle Hamiltonian for open systems with full Coulomb interaction: Application to classical and quantum time-dependent simulations of nanoscale electron devices

A many-particle Hamiltonian for a set of particles with Coulomb interaction inside an open system is described without any perturbative or mean-field approximation. The boundary conditions of the Hamiltonian on the borders of the open system [in the real three-dimensional (3D) space representation] are discussed in detail to include the Coulomb interaction between particles inside and outside of the open system. The many-particle Hamiltonian provides the same electrostatic description obtained from the image-charge method, but it has the fundamental advantage that it can be directly implemented into realistic (classical or quantum) electron device simulators via a 3D Poisson solver. Classically, the solution of this many-particle Hamiltonian is obtained via a coupled system of Newton-type equations with a different electric field for each particle. The quantum-mechanical solution of this many-particle Hamiltonian is achieved using the quantum (Bohm) trajectory algorithm [X. Oriols, Phys. Rev. Lett. 98, 066803 (2007)]. The computational viability of the many-particle algorithms to build powerful nanoscale device simulators is explicitly demonstrated for a (classical) double-gate field-effect transistor and a (quantum) resonant tunneling diode. The numerical results are compared with those computed from time-dependent mean-field algorithms showing important quantitative differences.