ProjectMABP – Mathematische Analyse des Bose Polarons

Basic data

Acronym:
MABP
Title:
Mathematische Analyse des Bose Polarons
Duration:
01/03/2024 to 28/02/2027
Abstract / short description:
At very low temperature, a gas of Bosonic atoms undergoes a phase transition to a Bose-Einstein condensate: a macroscopic number of particles exhibit collective quantum behavior. Introducing an impurity particle into the condensate can reveal many of its fundamental properties, and such coupled systems are expected to yield numerous applications in quantum engineering. At zero temperature, all particles of a non-interacting Bose gas will occupy the one-particle ground state. For weakly interacting systems, this ground state is modified and some particles occupy states of higher energy. The theory behind these excitations goes back to a seminal work of Bogoliubov from 1947, who showed that excitations typically appear in pairs, and described them in terms of a
quantum field. In this project we examine systems of many bosons with few impurities from a mathematical perspective. We will prove the validity of an effective model in which the impurities interact with Bogoliubov's excitation field. Recent results establish this model in the special case of a dense,
weakly interacting, homogeneous condensate on a torus. In order to cover more physical situations, we aim at generalizing them in two directions: First,
we will consider dilute gases, as they are typically used in experimental Bose-Einstein condensates. For such systems, interactions are very singular as
they are short range and strong. They induce a non-neglibible correlation structure, requiring renormalization of Bogoliubov's theory. Second, we will
treat the physical situation of non-periodic systems. For extended systems, a detailed analysis of the relevant scales in space and time will allow for an
approximate reduction to the case of constant density. Combining insights on both questions will lead to a deeper understanding of Bogoliubov's approximation, which is an important model case for more general quasiparticle approximations in condensed-matter physics.
Keywords:
mean-field dynamics, Bogoliubov-Fröhlich

Involved staff

Managers

Department of Mathematics
Faculty of Science
SFB-TR 352 - Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
Collaborative research centers and transregios

Local organizational units

Department of Mathematics
Faculty of Science
University of Tübingen

Funders

Bonn, Nordrhein-Westfalen, Germany
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