Simulation of Solid-State Structures with a Single Electron

The milestone of the correct simulation of a single electron is to exclude its action upon itself. Only the field created by the environment should be involved into the evolution equation. Two different approaches to cope with the problem are discussed, outlining their advantages and drawbacks. The first strategy is based on the response of environment to the fictitious charge density e|ψ|2 (ψ is a wave-function). This is a fundamental of the theory of polaron. The second strategy is based on the response of environment to a point charge. This approach completely denies an existence of polarons. We propose an experiment with quantum oscillations in a double quantum dot to distinguish what approach is true. The related problem of how to keep only one electron in a dot for fairly long time and distinguish whether the dot is occupied or empty is also regarded and the relevant conditions are derived.