TY  - JOUR
AU  - Belitsky, V.
AU  - Schütz, G. M.
TI  - Duality, supersymmetry and non-conservative random walks
JO  - Journal of statistical mechanics: theory and experiment
VL  - 2019
IS  - 5
SN  - 1742-5468
CY  - Bristol
PB  - IOP Publ.
M1  - FZJ-2019-04592
SP  - 054004
PY  - 2019
AB  - We derive a probabilistic interpretation of the observation that the quantum XY chain is supersymmetric in the sense that the Hamiltonian commutes with the generators of a subalgebra of the universal enveloping algebra of the Lie superalgebra and its deformations. The XY chain is shown to be the generator of a Markov process that describes classical vicious random walkers that annihilate immediately when they arrive on the same site, while new random walkers are created at neighbouring sites. The supersymmetry leads to a probabilistic self-duality relation and a duality between the random walk model with an even and odd number of particles, respectively.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000468501000001
DO  - DOI:10.1088/1742-5468/ab14d6
UR  - https://juser.fz-juelich.de/record/865027
ER  -