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Universität Augsburg
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Universität Augsburg
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Professor Dr. Gunter Schütz
Lissabon
spricht am
Mittwoch, 9. Dezember 2026
um
14:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| The symmetric Dyson exclusion process (SDEP) is a stochastic interacting particle system with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric simple exclusion process and as a discrete version of Dyson’s Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. This allows for proving an explicit formula for the time evolution of the expected microscopic particle density. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling and non-local hydrodynamics where the current is a genuinely non-local functional of the density given by a Hilbert transform. This non-local one-field description is equivalent to a local complex Burgers equation for finite particle density. Closed evolution formulas allow us to solve the melting of single and double block initial states, producing limit shapes and arctic curves that agree with large-scale Monte Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Stefan Großkinsky |