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Derivation of Maxwell's equations using mean field limits

Mathematical Physics & Probability

Speaker: Peter Pickl, Mathematisches Institut der Universit√§t M√ľnchen
Location: 3106 MSB
Start time: Wed, Sep 28 2011, 4:10PM

The usual textbook argument, showing that Maxwell's equations are a consequence of QED, are the Heisenberg equations for the quantized A and E fields. But there are situations where Maxwell's equations do not describe the physical system (photoeffects, systems with entanglement between the charged particles and the field). Therefore such a general argument is questionable.
In the talk I will present a rigorous derivation of Maxwell's equations for the special situation of many nonrelativistic charged particles which initially form a BEC coupled to the photon field where the photons are initially in some coherent state. I will show that the bosons will stay close to a product state which solves Hartree coupled to the Maxwells equation as time evolves. I will give reasons, why the given argument does not apply to situations, where Maxwell's equations are in fact not valid.