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Lecturer
Serena Cenatiempo serena.cenatiempo@gssi.it
Course Description
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we will explore this challenge in the case of the interacting Bose gas, a system whose low-temperature phases exhibit the so-called Bose-Einstein condensation phenomenon, a phase of matter in which particles remain confined purely due to quantum effects. In particular, we will discuss how the non-linear Hartree and Gross-Pitaevskii equations arise as effective descriptions for the dynamics of a large number of particles exhibiting condensation, in relevant scaling regimes. Time permitting, we will also discuss how quantum fluctuations around the condensate can be accurately described by the so-called Bogoliubov theory.
Course requirement
Basic elements of the theory of linear operators in Hilbert spaces.
The knowledge of the formalism Quantum Mechanics may be helpful, but it is not required.
Calendar:
The course will consists of 6 lectures, scheduled as follows:
Wed, Sep. 23: 9.00 - 10.30
Thu, Sep. 24: 9.00 - 10.30
Mon, Sep. 28: 9.00 - 10.30
Wed, Sep. 30: 9.00 - 10.30
Wed, Oct. 7: 9.00 - 10.30
Thu, Oct. 8: 9.00 - 10.30
Connections with other courses
Introduction to the non linear Schrödinger Equation
Dynamics of Open Quantum Systems
Mathematical Construction of Interacting Bosonic Theories
Lecture Notes