Topological Subordination in Quantum Mechanics

An example of non-Markovian quantum dynamics is considered in the framework a geometrical (topological) subordination approach. The specific property model that it coincides exactly with fractional diffusion equation, which describes geometric Brownian motion on combs. Both classical and are described using dilatation operator xddx. Two examples subordinators considered. first one Gaussian function, due to comb geometry. For consideration choice initial conditions, corresponds integral representation Mittag–Leffler function by means integral. second subordinator Dirac delta results from memory kernels define time derivatives equation.