6,492 research outputs found
Permutability graphs of subgroups of some finite non-abelian groups
In this paper, we study the structure of the permutability graphs of
subgroups, and the permutability graphs of non-normal subgroups of the
following groups: the dihedral groups , the generalized quaternion groups
, the quasi-dihedral groups and the modular groups .
Further, we investigate the number of edges, degrees of the vertices,
independence number, dominating number, clique number, chromatic number, weakly
perfectness, Eulerianness, Hamiltonicity of these graphs.Comment: 35 pages, 1 figur
From quantum stochastic differential equations to Gisin-Percival state diffusion
Starting from the quantum stochastic differential equations of Hudson and
Parthasarathy (Comm. Math. Phys. 93, 301 (1984)) and exploiting the
Wiener-Ito-Segal isomorphism between the Boson Fock reservoir space
and
the Hilbert space , where is the Wiener probability measure of
a complex -dimensional vector-valued standard Brownian motion
, we derive a non-linear stochastic Schrodinger
equation describing a classical diffusion of states of a quantum system, driven
by the Brownian motion . Changing this Brownian motion by an
appropriate Girsanov transformation, we arrive at the Gisin-Percival state
diffusion equation (J. Phys. A, 167, 315 (1992)). This approach also yields an
explicit solution of the Gisin-Percival equation, in terms of the
Hudson-Parthasarathy unitary process and a radomized Weyl displacement process.
Irreversible dynamics of system density operators described by the well-known
Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by
coarse-graining over the Gisin-Percival quantum state trajectories.Comment: 28 pages, one pdf figure. An error in the multiplying factor in Eq.
(102) corrected. To appear in Journal of Mathematical Physic
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