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Course requirements and suggested sequencing

To complete a student’s undergraduate training in classical and quantum physics, students are required to take 4 graduate courses. These are one-term classroom courses, typically 30 hours of classes and labs. Most graduate courses will have a seminar component. The topics of graduate courses may vary from term to term, however our system does not permit students to repeat the same course with a change in topic. Moreover, it is unreasonable to attend courses you have already covered elsewhere; this does not advance your skills. Two courses must be completed in the first year of graduate study and the remaining two in the second year, but a different sharing (e.g. 3+1) is also possible. The final exams must be registered with satisfactory grades (High Pass on average over the first two years is strongly advised in order to get a good record when admitted to candidacy). Since the starting date of the PhD is now October 1st., registration of the exams must be completed no later than July the 31st in order to allow for the administrative procedures to be admitted to the next year.Arrabbiato

To gain the maximum benefits from each course it is important that students see the courses in conjunction with the kind of research training they are taking. Responsibility lies with each student (and their adviser) to think about what research they wish to conduct, what methods might be amenable, their own methodological competence, and therefore which courses to attend. Graduate Students should take a broad view of the courses and the opportunities they offer. Their purpose is to give students an awareness of, and experience in using a wide range of research methods and concepts in Physics. 

Course enrollment procedures

Once the list of activated courses is made public by the Coordinator, the students are asked to present a plan of study and to enroll within a given dealine. An Audit requires regular attendance and any other obligations as stated by the course instructor. If these requirements are not met, the audit will be removed from the students record at the instructors request. It is the student’s responsibility to collaborate with her/his fellow students in reaching a rapid decision on course enrolling. For assistance in enrolling in courses, students are advised to contact the PhD Coordinator and their graduate student representatives who will prepare the option scheme and bring it to the attention of the Graduate School Board.

Taking courses outside the Physics Department

With the approval of the Graduate School Board it is possible to replace one of the required four advanced courses with a graduate course carried out in another Graduate School. According to the new DM 226/2021, it is not anymore possible to replace a PhD course with a course of the Laurea Magistrale.

In occasional circumstances, a student can take one Graduate course in a qualified research center abroad. If the student is under an international co-tutèle agreement with another Graduate School then all Term Advanced Courses can be taken abroad. In this latter case, a course certification and the corresponding grade must be submitted to the Coordinator and to the Graduate Registrar (Mrs. Anna Rita Mangia).

Here is the list of advanced courses organized by our Graduate School in the academic year 2023/2024. All courses have been chosen by at least 3 PhD students and are therefore activated (except the Schools, which take place anyway). Note that most courses are activated every two years. Please ask the indicated responsibles for additional infomation on each course. Guidelines for teachers of PhD courses

  • Quantum machine learning and applications in physics (D. Gerace): syllabus 
  • Soft skills for graduate students (A. Bacchetta, G.F. Mancini): syllabus
  • Strong interactions (B. Pasquini, M. Radici): syllabus
  • Introduction to thermal quantum field theory (C. Dappiaggi): syllabus
  • Stochastic thermodynamics in open quantum systems (G. Guarnieri): syllabus
  • Photonics: theory and computational methods (L. Andreani): syllabus
  • Ultrafast laser physics (G. F. Mancini): syllabus
  • Physics of massive neutrinos (A. Menogolli): syllabus
  • Models in biomedical physics: from in vitro cell systems to population studies (N. Protti, G. Baiocco): syllabus
  • Geant4 School (M.P. Carante, I. Postuma): syllabus
  • International School on plasmonics and nano-optics (L. Andreani): syllabus 


Here is the list of advanced courses organized by our Graduate School.  The tagged ones were activated for the academic year 2022/2023. Note that most courses are activated every two years.   Guidelines for teachers of PhD courses

  • Machine learning applications in Physics (Rebuzzi, Negri, Ngadiuba): syllabus
  • Advanced theory of solids (Andreani): syllabus
  • Mathematical aspects of quantum field theory (Dappiaggi): syllabus
  • Experimental particle physics (Rebuzzi, Negri): syllabus
  • Generation and manipulation of nonclassical states of light for quantum technologies (Galli, Liscidini): syllabus
  • Geant4 school (Bortolussi, Postuma): syllabus
  • Soft skills (Mancini, Prando): syllabus

Below there is a list of courses activated in the previous academic years with related syllabi. We are working on renovating the teaching system of the PhD school, following the new rules imposed by DM 226/2021 and Regolamento.  A new website is under preparation.

  • Basic - Python-based Methods and Applications in Physics (A. Negri)
  • Theo - Computational Methods in Theoretical Physics
  • Theo - Relativistic Quantum Field Theory
  • Theo - Advanced Quantum Information (A. Tosini)
  • Theo - Selected Topics in Quantum Mechanics
  • Theo - Strong Interactions (B. Pasquini, M. Radici)
  • Theo - Nuclear Structure
  • Theo - Electroweak and QCD Field Theories
  • Theo - Advanced Theory of Solids
  • Theo - Photonics: theory and computational methods (D. Gerace)
  • Theo - Open Quantum Systems
  • Theo - Mathematical Introduction to Fluid Dynamics
  • Theo - Advanced General Relativity
  • SPECIAL TOPICS COURSE: Quantum Computing
  • SPECIAL TOPICS COURSE: Ionizing Radiation and Biological Structures - Theory and Applications
  • Expt - Imaging and Mapping in Applied Physics (A. Lascialfari, M. Patrini)
  • Expt - Spectroscopies and Photonics
  • Expt - Magnetic Resonance Techniques in Solid-State Physics
  • Expt - Ultrafast Laser Physics (G.F. Mancini)
  • Expt - Experimental Particle Physics
  • Expt - Experimental Nuclear Physics
  • Expt - Radiation and Particle Detection
  • Expt - Information and Data Analysis
  • Expt - Physics of Massive Neutrinos (A. Menegolli)
  • Expt - Neutrino Phenomenology and Astroparticle Physics
  • Special elective course on Project Management (see below)
  • Special elective course on Entrepreneurship for physicists (see below)
  • Special elective course on Soft Skills (A. Bacchetta, G.F. Mancini)

In addition, some courses from IUSS may be mutuated. Please contact the Coordinator for details. 

Special Topics Courses

In the above list there are a number of SPECIAL TOPICS COURSES, these are courses including an intensive educational program, one to two weeks long, providing experience in specialized research techniques with lecture and laboratory courses in topics of current high interest. The Special Topics Courses are:

  • Quantum computing

The course aims at providing an introduction to the very hot topic of quantum computing, from the theoretical bases to main applications. It was activated for PhD students in the academic year 2018/2019. For complete info see the dedicated web page. 

  • Biophysics on Neural Signaling 

This course is mutuated from the course "Neuroscienze" to be held at Collegio Borromeo. Please see web site of Collegio Borromeo for updated details.

  • Ionizing Radiation and Biological Structures: Theory and Applications

This is an advanced course on the interaction between biological structures and ionizing radiation. In the last year the course has been integrated with the special topic course Modeling radiation effects from initial physical events  (Pavia, end of May-beginning of June), dedicated to learning modeling approaches and techniques in radiation biophysics and radiobiology research, from basic mechanisms to applications. Please contact prof. Andrea Ottolenghi for details.

Additional Elective Courses

The following courses do not belong to the strict course requirements for the PhD in Physics, however their attendance is strongly recommended.

  • Soft skills. This course is offered for the academic year 2020/2021. It consists of lectures and hands-on dealing with "Presentation making" by prof. Alessandro Bacchetta, lectures/seminars will also be organized on other topics (e.g. self-awareness, entrepreneurship, technological transfer).
  • Project Management. This mini-course is held on January 31, February 1-7-8, 2019. It will be given by experts from IBM. See the programme.

The 2017 course has been successfully completed! Download slides and selected feedback from students

The course is given by prof. Davide Iannuzzi (Vrije Universiteit, Amsterdam). It has the following goals: (1) To make students appreciate the advantages offered by a more entrepreneurial attitude towards technology transfer opportunities; (2) To present the most basic tools that allow entrepreneurs to bring new ideas to market; (3) To give students the opportunity to appreciate the differences and analogies between problem solving in physics and problem solving in business. Lectures are held in January 2017 on Wednesday 25 (17-18 pm, aula 101), Thursday 26 (9-10 am and 14.30-15.30 pm, aula 102) and Friday 27 (9-11, aula 102). The course is complemented by the PhD colloquium of prof. Iannuzzi, Thursday 26 at 16 pm, aula 102.

The following courses are organized by the SAFD (the Graduate School of the University) and they are offered to all PhD students of the University of Pavia.

  • Linguaggi, problemi e metodi della comunicazione scientifica (LCS) The course is not activated for 2019/2020.

The course is held in the II term at Collegio Nuovo and it consists of the following modules: Presentation making, Public speaking, I fondamenti della comunicazione, Scrittura per facoltà scientifiche.

  • Imparare a progettare in Europa 

The course deals with project writing and managing in European context (Horizon 2020 program). The 2015 course has been held in the month of February 2015 at the Physics Department. Updated news on the 2016 course will be published on the web page of the Graduate School of the University . The last edition of the course has been held in June 2017.

2015 Course completed, see dedicated web page

Other courses for PhD students are organized within the University of Pavia: please see the UNIPV web page for details


Here we shall briefly illustrate the advanced courses offered by the Graduate School in Physics. Each course has a responsible, who is the faculty member the graduate student have to contact for further details on the structure of the course. The responsible organizes the course by coordinating the various instructors and possible special topics seminars. 

Python-based Methods and Applications in Physics

Introduction to Python: basics, simple exercises, notebooks, google Colab, examples of applications to data analysis and to machine learning. Highly recommended for all PhD students. 

  • Coordinator: Andrea Negri
  • Instructors: Andrea Negri, Marco Piastra (UniPV Engineering), other colleagues

Computational Methods in Theoretical Physics

The course, "problem solving" oriented, will deal with the solution of theoretical problems using several Monte Carlo techniques. The programming language will be Python. No special prerequisites (e.g. knowledge of specific coding languages) are required, although this will not be a course on programming. The topics will go from Classical Molecular Dynamics to Lattice Gauge Theories, passing through Random Walk, Self Avoiding Walk, Percolation, Ising Model. 

  • Coordinator: M. Guagnelli
  • Instructors: M. Guagnelli

Highlight (2/2/2018): As an outcome of this course, four graduate students (cycle 30, now Doctors) set up a working group and wrote a paper on a Python implementation of the Γ-method for Monte Carlo simulations, which has been published in Computer Physics Communications.

Relativistic Quantum Field Theory

This is an advanced course in quantum field theory tailored on those students interested
in theoretical high energy physics. Arguments range from methods in relativistic quantum field theory to particle physics phenomenology.

  • Coordinator: F. Piccinini
  • Instructors: F. Piccinini, G. Montagna, Seminars 

Quantum Information Science

This is an advanced course in quantum information science. Quantum Information has become a large interdisciplinary developing area in Physics. "Information" is a new unifying paradigm, to the extent that quantum-mechanical phenomena are now regarded as inevitable consequences of information-theoretic considerations. The new quantum protocols and algorithms are now part of the everyday physics language, with computer science and information theory now entering the realm of foundations. Unique is the opportunity of working in hi-tech and, at the same time, being involved in fundamental problems. The protocols of quantum teleportation, cryptography, and Shor's algorithms have changed our way of thinking physics.

  • Coordinator: M. D’Ariano.
  • Instructors: M. D’Ariano, C. Macchiavello

Selected Topics in Quantum Mechanics

This is an advanced course on selected arguments in quantum mechanics. Quantum Foundations has recently become a main topic in advanced theoretical institutes, with a new focus on the derivation of Quantum Theory from general principles, and on novel frameworks and interpretations, such as the informational and Bayesian ones, along with powerful new approaches to entanglement and nonlocality coming from Quantum Information. On the other hand, the debate on realism and completeness has recently entered the realm of general probabilistic theories, entering also the relativistic context and the foundations of quantum field theory.

  • Coordinator: M. D’Ariano
  • Instructors: M. D’Ariano, C. Macchiavello

Strong Interactions

This is an advanced course in hadronic physics.

  • Coordinator: M. Radici, B. Pasquini
  • Instructors: M. Radici, A. Bacchetta, B. Pasquini, Seminars

Nuclear Structure

This is an advanced course in nuclear theory. Typical topics are: nuclear models, nuclear force, nuclear reaction and electromagnetic probes.

  • Coordinator(s): C. Giusti
  • Instructors: C. Giusti

Electroweak and QCD field theories

This is an advanced course on phenomenological aspects of the Standard Model and beyond. Some of the topics covered in the lectures will be: calculation of one-loop electroweak and QCD corrections, higher-order loop calculations (introduction), subtraction methods, parton showers, NLO-PS matching techniques.
  • Coordinator: O. Nicrosini
  • Instructors: F. Carloni Calame, M. Chiesa, Seminars

Advanced Topics in Quantum Field Theory

Joint course in theoretical and mathematical physics, with contributions from colleagues and guests. Highly recommended for PhD students of theoretical and mathematical area.

  • Coordinator(s): C. Dappiaggi
  • Instructors:  C. Dappiaggi,  colleagues, Seminars

Mathematical introduction to fluid dynamics

Goal of the course is to give an introduction to the basic, structural aspects of fluid dynamics. To start with the Euler equations for an inviscid fluid will be derived from first principles and explicit solutions will be constructed in the case of a two-dimensional, incompressible fluid. Subsequently we will discuss the role of viscosity and the associated Navier-Stokes equations. We will construct a few solutions in highly simplified scenarios and we will outline the main difficulties in providing a thorough analysis in the case of a three-dimensional viscous fluid. In the last part of the course, we will apply the mathematical concepts developed in the first part to the theory of the lift force and to that of shock waves..

  • Coordinator(s): C. Dappiaggi
  • Instructors:  C. Dappiaggi
  • Bibliography: A. J. Chorin and J. E. Marsden, "A Mathematical Introduction to Fluid Mechanics (2000) Springer"

Relativistic cosmology

In this series of lectures, I will address both foundational themes, such as what issues a theory of cosmology deals with, and themes that have emerged during the present "golden age of discovery".  We will discuss the interpretation of the Cosmological Principle and introduce the cosmological standard model (associated with the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime), with a selection of its many predictions and current problems: Dark energy, the nature of the Big Bang, structure formation. If time permits, we will touch upon theories of the early universe, from inflation to speculation.

Previous knowledge of general relativity is not assumed. I will provide the necessary study material in the form of lecture notes.

  • Coordinator(s): M. Carfora
  • Instructors:  M. Carfora


This is an advanced course dealing with methods of theoretical physics applied to economy. Mutuated from the course in the Laurea Magistrale. The course is starting in October, please contact prof. Montagna as soon as possible if you wish to attend!

  • Coordinator: G. Montagna
  • Instructors: G. Montagna, G. Bormetti, seminars

Advanced Theory of Solids

This is an advanced course on solid state theory. Topics include: elementary excitations  (plasmons, excitons, polaritons, ...), advanced quantum treatment of electronic systems, photovoltaic cells, and the like.

  • Coordinator: L.C. Andreani
  • Instructors: L.C. Andreani, other colleagues, Seminars

Photonics: Theory and Computational Methods

This is and advanced course on photonics and nanophysics. Topics include: nanophotonic systems (e.g. photonic crystals), computational methods - theory and tutorials, quantum effects in radiation-matter interaction, non-linear optics.

  • Coordinator: D. Gerace
  • Instructors: D. Gerace, L.C. Andreani, M. Liscidini, seminars

Open Quantum Systems

This is an advanced course on the analysis of analytical and numerical techniques for the study of interacting quantum systems.

  • Coordinator: L. Maccone
  • Instructors: L. Maccone

Biophysics on Neural Signaling

The course is offered under the aegis of a collaboration between our graduate school and the graduate school in physiology and neuroscience. The computational problems that are solved by networks of neurons, from roughly 100 cells in a small worm to 100 billion in humans provide a number of challenging problems to physicists.
Careful study of the natural context for these tasks leads to new mathematical formulations and physical modeling of the problems that brains are solving, and these theoretical approaches in turn suggest new experiments to characterize neurons and networks. This interplay between theory and experiment is the central theme of this course. The course will start from a description of the biomolecular structure of the neuronal membrane and will provide a biophysical interpretation of the processes generating electrical activity in neurons and synapses. The target is to illustrate how neurons generate information codes and how these are processed in complex neuronal networks. Topics will include: 1) Biophysical phenomena in the neuronal membrane, 2) Information in spike trains, 3) Principles of signal processing in neuronal networks.

For the academic year 2014/2015 thr course is mutuated from the course "Neuroscienze" to be held at Collegio Borromeo in Fall 2015. Please see web site of Collegio Borromeo for updated details.

  • Coordinator: E. D’Angelo
  • Instructors: E. D’Angelo

Imaging for Biomedical Applications

This is an advanced course on imaging techniques applied to problems in biomedical physics.

  • Coordinator: A. Ottolenghi
  • Instructors: A. Ottolenghi

Ionizing Radiations and Biological Structures: Theory and Applications

This is an advanced course on the interaction between biological structures and ionizing radiation. The course will be integrated with the special topic course Modeling radiation effects from initial physical events, (Pavia, end of May - beginning of June), dedicated to learning modeling approaches and techniques in radiation biophysics and radiobiology research, from basic mechanisms to applications.

  • Coordinator: A. Ottolenghi
  • Instructors: A. Ottolenghi

Spectroscopies and Photonics

This is an advanced course on spectroscopic techniques and photoncis in condensed matter physics. Topics will include: (i) optical spectroscopies: techniques and experiments; (ii) educational kit on integrated optics (in collaboration with Cork Institute of Technology), (iii) quantum photonics experiments in the new lab.

  • Coordinator: F. Marabelli.
  • Instructors: F. Marabelli, M. Galli.

Magnetic Resonance Techniques in Solid-State Physics

The aim of the course is to introduce the basic aspects of magnetic resonance techniques, including nuclear magnetic resonance spectroscopy and imaging, muon and electron spin resonances, and to present paradigmatic examples of their recent applications to condensed matter physics as well as to the biomedical sector.

  • Coordinator: P. Carretta
  • Instructors: P. Carretta

Experimental Particle Physics

This is an advanced course on modern particle physics with a particular attention to collider physics.

  • Coordinator: D. Rebuzzi, A. Negri
  • Instructors: D. Rebuzzi, A. Negri, Seminars

Experimental Nuclear Physics

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Download this file (1-Iannuzzi_why_bother.pdf)1-Iannuzzi-why-bother 2497 Kb01/29/17 16:39
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Download this file (Case_study_Iannuzzi.pdf)Case_study_Iannuzzi.pdfCase study for the course by Davide Iannuzzi3405 Kb11/16/16 10:16
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