4,623 research outputs found
Bilayers in Four Dimensions and Supersymmetry
I build superstrings in out of purely geometric bosonic
data. The world-sheet is a bilayer of uniform thickness and the
supercharge vanishes in a natural way.Comment: 4 pages,Latex, no figur
Markov Chains and Dynamical Systems: The Open System Point of View
This article presents several results establishing connections be- tween
Markov chains and dynamical systems, from the point of view of open systems in
physics. We show how all Markov chains can be understood as the information on
one component that we get from a dynamical system on a product system, when
losing information on the other component. We show that passing from the
deterministic dynamics to the random one is character- ized by the loss of
algebra morphism property; it is also characterized by the loss of
reversibility. In the continuous time framework, we show that the solu- tions
of stochastic dierential equations are actually deterministic dynamical systems
on a particular product space. When losing the information on one component, we
recover the usual associated Markov semigroup
Stochastic Master Equations in Thermal Environment
We derive the stochastic master equations which describe the evolution of
open quantum systems in contact with a heat bath and undergoing indirect
measurements. These equations are obtained as a limit of a quantum repeated
measurement model where we consider a small system in contact with an infinite
chain at positive temperature. At zero temperature it is well-known that one
obtains stochastic differential equations of jump-diffusion type. At strictly
positive temperature, we show that only pure diffusion type equations are
relevant
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
From n+1-level atom chains to n-dimensional noises
In quantum physics, the state space of a countable chain of (n+1)-level atoms
becomes, in the continuous field limit, a Fock space with multiplicity n. In a
more functional analytic language, the continuous tensor product space over R
of copies of the space C^{n+1} is the symmetric Fock space Gamma_s(L^2(R;C^n)).
In this article we focus on the probabilistic interpretations of these facts.
We show that they correspond to the approximation of the n-dimensional normal
martingales by means of obtuse random walks, that is, extremal random walks in
R^n whose jumps take exactly n+1 different values. We show that these
probabilistic approximations are carried by the convergence of the basic matrix
basis a^i_j(p) of \otimes_N \CC^{n+1} to the usual creation, annihilation and
gauge processes on the Fock space.Comment: 22 page
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