The Mathematical Physics group was born at the Mathematics Department “V. Volterra” of the University of Ancona (subsequently Department of Mathematical Sciences of the Marche Polytechnic University, since 2011 part of the Department of Industrial Engineering and Mathematical Sciences). Several people took part in this group in the past (among others Sandro Graffi, Luisa Arlotti, Riccardo Ricci, Laura Gardini, Giovanni Frosali, Renzo Lupini, Giampiero Spiga, Giorgio Busoni). Now the group consists of only one associate professor, whose research interests lie within the fields of quantum and classical kinetic theory, numerical methods in transport theory, perturbation methods and other analytical and numerical methods in the study of some mechanical systems.
Both research and teaching activities are pursued by the group.
The teaching activity concerns courses of Theoretical Mechanics, Calculus 1 and 2, Numerical Analysis, Probability and Statistics for the engineering degree courses in Ancona and Fermo. The research activity concerns quantum transport (in particular the Wigner-function approach) and the mathematical modelling of some mechanical systems by analytical and numerical methods.
Research is being pursued along two main lines:
Quantum transport problems in semiconductors by the Wigner-function approach. The Wigner function approach allows the use of phase space concepts in quantum transport; this entails the possibility of adopting well established techniques and methodologies of classical transport in the quantum case. The Wigner-function based models for semiconductors formulated so far, however, are applicable only to an infinite medium and to a parabolic band profile. The research activity of the group in this area aimes at extending the Wigner-function approach to particle ensembles confined within bounded domains and with non-parabolic band profiles.
Modelling of some mechanical systems by analytical and numerical methods. One topic under investigation in this area is the study of moving-boundary problems for the Klein-Gordon equation on a half-line, with the inclusion of nonlinear terms and harmonic excitations. Mostly perturbation techniques are being used. The main motivation and application is in the “J-lay problem”, relevant to several engineering applications (e.g., lying of cables and other flexible structures on the seabed; railway tracks dynamics). Another topic in this area is the study of the dynamics of an inverted pendulum between rigid walls, with harmonic and superharmonic excitations, and with attention to chattering phenomena.