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Killing versus branching: Unexplored facets of diffusive relaxation
Piotr Garbaczewski1, Mariusz Żaba1
1Institute of Physics, <a href="https://ror.org/04gbpnx96">University of Opole</a>, 45-052 Opole, Poland.
Abstract:
We analyze the relaxation dynamics of Feynman-Kac path integral kernel functions, in terms of branching diffusion processes with killing. This amounts to the killing versus branching approach to path integration, which seems to be a novelty in the pathwise description of conditioned Brownian motions and diffusion processes with absorbing boundaries. There, Feynman-Kac kernels appear as building blocks of inferred (Fokker-Planck) transition probability density functions. A consistent probabilistic meaning is hereby provided (killing versus branching time rate) to bounded from below Feynman-Kac potential functions, which instead of being positive-definite (a standard killing paradigm), may take negative values on bounded spatial subdomains (that inflicts trajectory branching).
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