Mitia Duerinckx: Quantum diffusion and related questions

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In this talk, we discuss a spectral perspective on the quantum diffusion conjecture for a quantum particle in a weakly random medium. We also draw the link to the study of Cherenkov radiation or friction effects for several translation-invariant QFT models that describe a non-relativistic quantum particle interacting with a quantized relativistic field of bosons. By a suitable fibration, those different problems are reduced to the metastability of the embedded mass shell of the free quantum particle, which is then naturally handled by means of Mourre's commutator method. However, regularity issues are known to be inherent to QFT models, due to their infinite dimensionality, thus challenging the application of Mourre's method. We introduce a non-standard construction of Mourre conjugate operators, which differs from second quantization. This leads us to several new results — although our findings remain partial in case of quantum diffusion. This is based on joint work with C.Shirley.

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