Transient Quantum Particle Attributes

Abstract

The transient problem is characterized by an in time developing Wigner state, determined by an initial condition - the Wigner function at a given initial time. Transient quantum algorithms are based on a further development of the concepts of signed particles, introduced for the stationary counterpart Chap. 14. A transition from a single to an ensemble particle picture is now imposed by the existence of a fixed time origin. All particles in the ensemble must be evolved synchronously to contribute at a given instant of time to the time dependent physical averages. Accordingly, particle annihilation can occur at for all particles equal evolution times. Another modified concept is the fundamental definition of a phase space. The momentum space becomes discrete, because a finite coherence length conforms the nanometer scale of the bounded domain of nowadays devices. This imposes to introduce semi-discrete Wigner function, potential, and equation. A Monte Carlo analysis provides the rules for the semi-discrete evolution of the numerical particles. The derived Signed-Particle algorithm, being a typical representative of the signed-particle approach, bears the same name. In the case of a constant electric field the Boltzmann and the Wigner equations become equivalent. This evolution duality offers an excellent opportunity for a proof of the concept. We show that the process of generation/annihilation of particles residing on discrete nodes of the momentum space is equivalent to the continuous Newtonian acceleration inherent to the Boltzmann equation.