Quantum Brownian Motion on noncommutative manifolds: construction, deformation and exit timesReportar como inadecuado



 Quantum Brownian Motion on noncommutative manifolds: construction, deformation and exit times


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We begin with a review and analytical construction of quantum Gaussian process and quantum Brownian motions in the sense of 25,10 and others, and then formulate and study in details with a number of interesting examples a definition of quantum Brownian motions on those noncommutative manifolds a la Connes which are quantum homogeneous spaces of their quantum isometry groups in the sense of 11. We prove that bi-invariant quantum Brownian motion can be deformed in a suitable sense. Moreover, we propose a noncommutative analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics for a specific example on noncommutative two-torus A{\theta}, which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that A{\theta} is a noncommutative model of the locally one-dimensional leaf-space of the Kronecker foliation.



Autor: Biswarup Das; Debashish Goswami

Fuente: https://archive.org/



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