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Quantum Hele-Shaw flow | | Haakan Hedenmalm
; Nikolai Makarov
; | | Date: |
19 Nov 2004 | | Subject: | Probability; Mathematical Physics MSC-class: 15A52; 62H20 | math.PR math-ph math.MP | | Abstract: | In this note, we discuss the quantum Hele-Shaw flow, a random measure process in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et al. This process arises in the theory of electronic droplets confined to a plane under a strong magnetic field, as well as in the theory of random normal matrices. We extend a result of Elbau and Felder to general external field potentials, and also show that if the potential is $C^2$-smooth, then the quantum Hele-Shaw flow converges, under appropriate scaling, to the classical (weighted) Hele-Shaw flow, which can be modeled in terms of an obstacle problem. | | Source: | arXiv, math.PR/0411437 | | Services: | Forum | Review | PDF | Favorites | |
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