Theoretical physics and complex systems




Noise and information, often believed to be opposite notions, have a common denominator: stochastic processes. Depending on his interest, an observer may regard a stochastic process either as a noise or an information source. At the heart of any stochastic process is randomness, which naturally embeds the idea of “many possibilities”; hence the notion of complexity. In recent years, these concepts have been extended all the way down from the microorganism to the quantum scales, thus unveiling a variety of intriguing phenomena with applications to bio- and nano-technology.



  • Soft Matter

Stochastic processes: stochastic resonance, noise rectification, noise harvesting. Active matter: modeling, particle clustering and segregation, microfluidics. Disordered systems: anomalous diffusion, transport in crowded environments. Complex systems: coupled nonlinear oscillators, turbulence, multi-agent models.

  • Information Theory

Quantum stochastic maps: discrete and continuous channel; channel capacities, quantum error correcting theory, quantum cryptography.

Entanglement: classification and measures, distillation and dilution, stationarity in dynamical systems; relativistic properties.

Information geometry: geometric structure of statistical models, statistical inference and differential geometry; geometry of quantum states.



Typology CFU Course
Compulsory 30 Advanced electromagnetism (6 CFU)
Advanced physics laboratory (6 CFU)
Machine learning (6 CFU)
Solid state physics (6 CFU)
Theoretical physics (6 CFU)
Recommended 30 Advanced probability and stochastic processes (6 CFU)
Quantum field theory (6 CFU)
Statistical mechanics (6 CFU)
Quantum information (6 CFU)
Biological physics (6 CFU)
Elective 12 only Condensed matter theory (6 CFU)
General relativity (6 CFU)
Quantum computation (6 CFU)
Dynamic and stochastic optimization (6 CFU)

(*) Students are allowed to take up to 24 CFU, free of tuition fees, at the University of Milano (Università Statale) including courses, stages, and thesis preparation (see for details).


For any information about this track including specific choices of the modules please contact:

Fabio Marchesoni -