| Abstract: |
| Investigating mixtures of bosons and fermions is an active area of research in experimental physics for constructing and understanding novel quantum bound states. These ultra-cold Bose-Fermi mixtures are intrinisically different from gases with only bosons or fermions. Namely, they show a fundamental instability due to energetic considerations coming from the Pauli exclusion principle. Inspired by this activity in the physics community, recently we started exploring the mathematical theory of Bose-Fermi mixtures. In particular, we will describe results obtained with Cardenas, Miller and Mitrouskas inspired by recent experiments by DeSalvo et al. on mixtures of light fermionic atoms and heavy bosonic atoms. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, and as well as stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. |
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