The cancellation of most events this summer means that PhD students lose opportunities to learn about topics outside their home working group and to get to know other students and researchers. The main lectures in this summer school are an opportunity to learn about the mathematics of many-body quantum systems. Furthermore, all participants are invited to present their research in small online groups to get to know each other and chat informally ("virtual post session").
For whom? Students and researchers in mathematical physics from all directions (not necessarily quantum systems).
Lectures by: Marcin Napiórkowski (University of Warsaw), Benjamin Schlein (University of Zurich), Robert Seiringer (IST Austria), Jan Philip Solovej (University of Copenhagen)
Virtual poster session: open to all interested participants (not necessarily working on quantum systems). Younger participants are particularly encouraged to participate. Please read carefully the poster session concept before preparing your poster.
On both days, the program starts in the early afternoon (Italian time). The first afternoon concludes with a virtual poster session.
Friday, June 19, 2020: 14:00-15:00 lecture Solovej, 15:15-16:15 lecture Seiringer, 16:30-18:00 virtual poster session
Monday, June 22, 2020: 14:00-15:00 lecture Napiórkowski, 15:15-16:15 lecture Schlein
Please find below the abstracts of the lectures:
Jan Philip Solovej: Many body Bose gases and the Bogolubov approximation
I will give the basics of many-body quantum mechanics and in particular the case for Bose gases. I will introduce the method of second quantization. I will then discuss Bogolubov's approximation in his original formulation, where the many-body Hamiltonian is approximated by what is called a quadratic Hamiltonian. Quadratic Hamiltonians have equilibrium states that are quasi-free or Gaussian states characterized by satisfying Wick's relation. I will use this to reformulate the Bogolubov approximation in terms of a variational model.
Robert Seiringer: The excitation spectrum of weakly interacting bosons
Of particular relevance for an understanding of the low-temperature properties of a quantum system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system.
Marcin Napiórkowski: Bogoliubov Theory at Positive Temperatures
I shall discuss the homogeneous Bose gas at positive temperatures within Bogoliubov theory. The theory arises by restricting the Hilbert space to quasi-free states. I will introduce the free energy functional and discuss the existence of equilibrium states, phase diagram and critical temperature. Based on joint work with Robin Reuvers and Jan Philip Solovej.
Benjamin Schlein: Dynamics of a strongly coupled polaron
We are interested in the time-evolution of a Fröhlich polaron, describing an electron coupled to a quantised phonon field, with a large coupling constant $\alpha$. For product initial data, with a coherent cloud of phonons and with the electron minimising the corresponding energy, we construct an approximation of the evolution, valid up to times of order $\alpha^2$. The approximation is given in terms of a product state, evolved through the classical Landau-Pekar equations, adjusted by a Bogoliubov dynamics, taking quantum fluctuations into account. This is joint work with N. Leopold, D. Mitrouskas, S. Rademacher and R. Seiringer.
Registration with an email address is necessary to control access to the zoom channels. Please fill in the registration form (registration is closed now).
The entire program will be held using Zoom. If you participate in the poster session or give a lecture, you will need to create your own (free) Zoom account, install or update the app, and accomodate yourself with its operation before the program.
Lectures: The password will be provided by email to registered participants.
Virtual poster session: All participants who present a poster need to open their own Zoom channel for the time of their poster session (free zome basic account needed). To avoid interference by trolls, it is important that you set the password as communicated by email (same password as for the main lectures).
Please find below the list of registered participants who have agreed to their name being published.
18 further participants have registered.
For questions, please contact: niels.benedikter "[a t]" unimi.it
Università degli Studi di Milano
Dipartimento di Matematica "Federigo Enriques"
Via Cesare Saldini 50
20133 Milano, ITALY