Summer School
Concept Program Registration Zoom Participants Contact
June 19+22, 2020

Applications of Bogoliubov Theory

Mathematical Physics of Quantum Many-Body Systems

Online Summer School

June 19 + 22, 2020 (Friday and Monday)

Concept

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.

Program

You may download the slides of the lectures here: Solovej, Seiringer, Napiórkowski, Schlein.

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

Convert Italian time to your local time.

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

Registration with an email address is necessary to control access to the zoom channels. Please fill in the registration form (registration is closed now).

Zoom

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: All main lectures are held in the zoom meeting ID: 973 3987 5546. 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).

If you are presenting a poster using a free zoom basic account, your channel will automatically close after 40 minutes - just reopen it, participants will be able to reconnect with the same link/ID.

Participants

Please find below the list of registered participants who have agreed to their name being published.

  1. Chiara Boccato, IST Austria
  2. Krzysztof Myśliwy, IST Austria
  3. Arnaud Triay, LMU - München
  4. Oluwadara Ogunkoya, University of Alabama at Birmingham
  5. Daniele Dimonte, University of Basel
  6. Serena Cenatiempo, Gran Sasso Science Institute
  7. Jacob Fronk, Heidelberg University/University of Copenhagen
  8. Dario Feliciangeli, IST Austria
  9. Francesco Raso Stoia, Universitá degli Studi di Milano Bicocca
  10. Lea Boßmann, IST Austria
  11. Jinyeop Lee, Korea Institute for Advanced Study
  12. Gianfausto Dell'Antonio, Sissa
  13. Elliott Lieb, Princeton
  14. Martin Ravn Christiansen, LMU Munich
  15. Gustavo de Oliveira, Universidade Federal de Minas Gerais
  16. Gianluca Panati, "La Sapienza" University of Rome
  17. Ludwik Dabrowski, SISSA, Trieste
  18. Phan Thanh Nam, LMU Munich
  19. Paolo Facchi, Universita di Bari, Italy
  20. Daniele Valeri, University of Glasgow
  21. Giuseppe Gaeta, Università degli Studi di Milano
  22. Giuseppe Bevilacqua, Università di Siena
  23. Antonio Moscato, Trento University
  24. Chun Yin Lam, LMU Muenchen
  25. Nicolas Rougerie, Université Grenoble-Alpes & CNRS
  26. Vatsana Tiwari, Indian Institute of Science Education and Research, Bhopal, India
  27. Florian Haberberger, LMU Munich
  28. Nikolai Leopold, University of Basel
  29. Leonard Wetzel, LMU Munich
  30. Marcin Napiórkowski, University of Warsaw
  31. Benjamin Schlein, University of Zurich
  32. Robert Seiringer, IST Austria
  33. Jan Philip Solovej, University of Copenhagen
  34. Sabiha Tokus, Copenhagen University
  35. Oleksandr Stashko, Taras Shevchenko National University of Kyiv
  36. Oleh Savchuk, Taras Shevchenko National University in Kyiv
  37. Mukhayo Rasulova, Institute of Nuclear Physics Uzbekistan Academy of Sciences
  38. Slava Somsikov, Institute of Ionosphere
  39. Théotime Girardot, LPMMC
  40. Marcin Pruszczyk, University of Warsaw
  41. Konstantin Merz, TU Braunschweig
  42. DengLing Zhang, Xi’an University of Posts & Telecommunications
  43. Christian Hainzl, LMU Munich
  44. Ken Kim, LLNL/University of California
  45. Aamna Ahmed, IISER Bhopal ,India
  46. Michele Correggi, Politecnico di Milano
  47. Simone Rademacher, IST Austria
  48. Peter Hislop, Mathematics Department, University of Kentucky
  49. Andrea Moro, Università di Trento
  50. Christiaan van de Ven, Università di Trento
  51. Asbjørn Bækgaard Lauritsen, University of Copenhagen
  52. Emanuela Giacomelli, LMU Münich
  53. Soeren Petrat, Jacobs University Bremen
  54. Giulia Basti, University of Zurich
  55. Birger Brietzke, Heidelberg University
  56. Alex Gottlieb, Wolfgang Pauli Institute
  57. Søren Mikkelsen, University of Bristol
  58. Johan Jacoby Klemmensen, Ludwig Maximilian University
  59. Nilanjan Roy, Indian Institute of Science Education and Research Bhopal
  60. Luca Fresta, University of Zurich
  61. Andreas Deuchert, Institute of Mathematics, University of Zurich
  62. Davide Fermi, Scuola Normale Superiore
  63. Per Moosavi, ETH Zurich
  64. Alessandro Olgiati, CNRS Grenoble
  65. Chokri Manai, TU München
  66. Julien Ricaud, LMU (Munich)
  67. Marie Fialova, UCPH, QMATH
  68. Cristina Caraci, Gran Sasso Science Institute
  69. Johannes Agerskov, University of Copenhagen
  70. Luca Dellantonio, Institute for Quantum Computing
  71. Amanda Young, Technical University of Munich
  72. Amirali Hannani, Universite Paris Dauphine-PSL
  73. Igor Gapyak, Результати пошуку Результати веб-пошуку Taras Shevchenko National University of Kyiv
  74. Lukas Schimmer, University of Copenhagen
  75. Michał Pietruszka, University of Warsaw
  76. Per von Soosten, Harvard University
  77. Marcel Schaub, LMU Munich
  78. Frederik Ravn Klausen, University of Copenhagen
  79. Andrea Posilicano, Università dell'Insubria
  80. Robert Rauch, TU Braunschweig, Germany
  81. Li Chen, University of Mannheim
  82. Marcello Porta, SISSA

18 further participants have registered.

Contact

For questions, please contact: niels.benedikter "[a t]" unimi.it

Niels Benedikter
Università degli Studi di Milano
Dipartimento di Matematica "Federigo Enriques"
Via Cesare Saldini 50
20133 Milano, ITALY

www.nielsbenedikter.de