International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 07 | October-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET ISO 9001:2008 Certified Journal Page 1 A new analytical transport model for (nano) physics Paolo Di Sia 1 1 Adjunct Professor, Department of Philosophy, Education and Psychology, University of Verona, Italy ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - In this paper we focus on a new analytical transport Drude-Lorentz-like model, able to adjust previous unresolved problems and to present new interesting peculiarities. It works from sub-pico-scale to macro-scale and has a wide range of applications. Key Words: Mathematical Modelling, Analytical Calculus, Applied Analysis, Theoretical Physics, Nano-science, Nano-Bio-Technology. 1. INTRODUCTION In these years it has been performed a new generalization of the Drude-Lorentz model, based on the complete Fourier transform of the frequency-dependent complex conductivity ) (  of a system, which provides analytical expressions of the three most important quantities related to transport phenomena, i.e. the velocities correlation function T v t v    ) 0 ( ) (   at the temperature T, the mean squared deviation of position R 2 (t) and the diffusion coefficient D(t) [1]. The model avoids time-consuming numerical and/or simulation procedures and, in the case of nano-scale, it has been well tested and is useful both “a priori”, for searching new characteristics and peculiarities at nano-level, and “a posteriori”, for testing existing experimental data. It considers also quantum [2] and relativistic [3] effects. The comparison with existing models, like Drude-Lorentz and Smith models [4,5], has demonstrated a very good fit with current knowledge and is giving also interesting information’s about new behaviors at nano-scale, as damped oscillations at beginning of processes [6-11]. 2. TECHNICAL DETAILS The diffusion coefficients for nano-scale, of great importance for their connection with the sensitivity of nano-bio-devices, present the following analytical expressions.