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Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used also in the unbounded case, but rather little is known about the general form of unbounded generators. In this paper we first give a precise description of the standard form in the unbounded case, emphasizing intuition, and collecting and even proving the basic results around it. We also give a cautionary example showing that the standard form must not be read too naively. Further examples are given of semigroups, which appear to be probability preserving to first order, but are not for finite times. Based on these, we construct examples of generators which are not of standard form.
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigners approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called gen
We consider semigroups ${alpha_t: ; tgeq 0}$ of normal, unital, completely positive maps $alpha_t$ on a von Neumann algebra ${mathcal M}$. The (predual) semigroup $ u_t (rho):= rho circ alpha_t$ on normal states $rho$ of $mathcal M$ leaves invariant
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators
Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical entropy i
We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early