Abstract:

The Discrete State Simulation (DSS) has been developed to model heat and charge transport on a micron-scale with nanometer-resolution. Written in object-oriented code, the DSS is a coupled cellular automata simulator that builds upon the objects and rules of quantum mechanics. The DSS represents global non-equilibrium processes as patterns that emerge through an ensemble of scattering events that are localized at vibronic nodes. By tracking the energy-momentum-position coordinates of the individual particles that define the vibronic state at a node, the DSS undercuts equilibrium concepts such as temperature. Consequently, the DSS can represent physical systems that are described by more than one temperature or that contain physical features that defy definitions of temperature.

Using modified bootstrap sampling algorithms, the DSS depicted (1)?shifts in distribution functions induced by external fields and temperature gradients, (2)?field-dependent transitions from linear mobility to non-linear mobility, (3)?saturation velocities, (4)?non-exponential decay functions generated by multiple phonon scattering modes, and (5)?charge separations and electric potentials generated by temperature gradients. Ensemble averages were sensitive to the structure of dispersion relations, to the energy of the system, and to quantum coupling strengths.

Although the Discrete State Simulation requires more development before it becomes an engineering design tool, the reported research effort offers substantial justification for the development of object-oriented, discrete-state cellular automata. These computational machines would match the capabilities of conventional simulation techniques, and they would be able to address highly non-equilibrium situations by exercising dynamic rule construction--computational algorithms that evolve in response to the conditions that are being simulated.