2,736 research outputs found
Dynamical Semigroups for Unbounded Repeated Perturbation of Open System
We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies
generators which are related to evolution of an open system with a tuned
repeated harmonic perturbation. Our main result is the proof of existence of
uniquely determined minimal trace-preserving strongly continuous dynamical
semigroups on the space of density matrices. The corresponding dual W
*-dynamical system is shown to be unital quasi-free and completely positive
automorphisms of the CCR-algebra. We also comment on the action of dynamical
semigroups on quasi-free states
Conditions for strictly purity-decreasing quantum Markovian dynamics
The purity, Tr(rho^2), measures how pure or mixed a quantum state rho is. It
is well known that quantum dynamical semigroups that preserve the identity
operator (which we refer to as unital) are strictly purity-decreasing
transformations. Here we provide an almost complete characterization of the
class of strictly purity-decreasing quantum dynamical semigroups. We show that
in the case of finite-dimensional Hilbert spaces a dynamical semigroup is
strictly purity-decreasing if and only if it is unital, while in the infinite
dimensional case, unitality is only sufficient.Comment: 4 pages, no figures. Contribution to the special issue "Real-time
dynamics in complex quantum systems" of Chemical Physics in honor of Phil
Pechukas. v2: Simplified proof of theorem 1 and validity conditions clarifie
Complete positivity and neutron interferometry
We analyze the dynamics of neutron beams in interferometry experiments using
quantum dynamical semigroups. We show that these experiments could provide
stringent limits on the non-standard, dissipative terms appearing in the
extended evolution equations.Comment: 12 pages, plain Te
Structure of the Algebra of Effective Observables in Quantum Mechanics
A subclass of dynamical semigroups induced by the interaction of a quantum
system with an environment is introduced. Such semigroups lead to the selection
of a stable subalgebra of effective observables. The structure of this
subalgebra is completely determined
Quantum dynamical semigroups for diffusion models with Hartree interaction
We consider a class of evolution equations in Lindblad form, which model the
dynamics of dissipative quantum mechanical systems with mean-field interaction.
Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson
model. The existence and uniqueness of global-in-time, mass preserving
solutions is proved, thus establishing the existence of a nonlinear
conservative quantum dynamical semigroup. The mathematical difficulties stem
from combining an unbounded Lindblad generator with the Hartree nonlinearity.Comment: 30 pages; Introduction changed, title changed, easier and shorter
proofs due to new energy norm. to appear in Comm. Math. Phy
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