An Analytical Transport Model for Nanomaterials: The Quantum Version

Abstract

We have proposed a new model, generalizing the class of the Drude-Lorentz-like models, for describing the conductors in nanostructured form. Now we have performed the quantum version of this model, presenting an interesting mathematical elegance. This version is adequately inserted in the context of the already existing quantum models which regard this sector, and describes very well the dynamic behaviour, as extracted by time resolved techniques.

Nano-Modeling and Computation in Bio and Brain Dynamics

“…Research at the theoretical level help science in all sectors. Recently, a new analytical model that generalizes the Drude-Lorentz and Smith models for transport processes in solid-state physics and soft condensed matter has been used [ 21 , 22 , 23 ]. It provides analytical time-dependent expressions of the three most important parameters related to transport processes: The velocities correlation function of a system at the temperature T , from which it is possible to obtain the velocity of a carrier at generic time t ; The mean squared deviation of position R 2 ( t ), defined as , from which the position of a carrier in time is obtainable; The diffusion coefficient D , defined as , which gives important information about the temporal propagation of carriers inside a nanostructure [ 22 , 23 , 24 ].…”

“…The diffusion coefficient D , defined as , which gives important information about the temporal propagation of carriers inside a nanostructure [ 22 , 23 , 24 ].…”

A New Analytical Model for the Analysis of Economic Processes

“…A recent theoretical analytical formulation showed to fit very well experimental scientific data and offers interesting new predictions of various peculiarities in nanostructures [22][23][24].…”

“…Equations ( interesting peculiarities of the model is the "time domain" used approach, not previously found in such a contest, contrarily to the existing theoretical approaches of literature, which are "frequency domain" treatments and/or numerical methods [22][23][24].…”

Advances in Analytical Modelling for Nano-Bio-Technology

“…It avoids time-consuming numerical and/or simulation procedures, is mathematically very elegant and useful both for the study of new devices with desired characteristics and for testing and/or obtaining new values by existing experimental data. It considers also quantum [9] and relativistic [10] effects, the quantum relativistic step is in progress [11]. The comparison with existing utilized models, as Drude-Lorentz and Smith models [12] and the utilization of existing experimental data have demonstrated a very good fit with current knowledge [13][14][15][16][17][18][19] (Figure 1).…”