715,436 research outputs found
Long-time memory in non-Markovian evolutions
If the dynamics of an open quantum systems is non-Markovian, its {asymptotic}
state strongly depends on the initial conditions, even if the dynamics
possesses an {invariant} state. This is the very essence of memory effects. In
particular, the {asymptotic} state can remember and partially preserve its
initial entanglement. Interestingly, even if the non-Markovian evolution
relaxes to an equilibrium state, this state needs not be invariant. Therefore,
the non-invariance of equilibrium becomes a clear sign of non-Markovianity.Comment: 6 page
Isometries of almost-Riemannian structures on Lie groups
A simple Almost-Riemannian Structure on a Lie group G is defined by a linear
vector field (that is an infinitesimal automorphism) and dim(G) -- 1
left-invariant ones. It is first proven that two different ARSs are isometric
if and only if there exists an isometry between them that fixes the identity.
Such an isometry preserves the left-invariant distribution and the linear
field. If the Lie group is nilpotent it is an automorphism. These results are
used to state a complete classification of the ARSs on the 2D affine and the
Heisenberg groups
Equivalent Conditions for Irreducibility of Discrete Time Markov Chains
We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility, and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and assigns positive probability to all absorbing sets.
Involutory Hopf algebras and 3-manifold invariants
We establish a 3-manifold invariant for each finite-dimensional, involutory
Hopf algebra. If the Hopf algebra is the group algebra of a group , the
invariant counts homomorphisms from the fundamental group of the manifold to
. The invariant can be viewed as a state model on a Heegaard diagram or a
triangulation of the manifold. The computation of the invariant involves tensor
products and contractions of the structure tensors of the algebra. We show that
every formal expression involving these tensors corresponds to a unique
3-manifold modulo a well-understood equivalence. This raises the possibility of
an algorithm which can determine whether two given 3-manifolds are
homeomorphic.Comment: Figure 4 is missin
Comment on studying the corrections to factorization in B -> D(*) X
We propose studying the mechanism of factorization in exclusive decays of the
form B->D(*)X by examining the differential decay rate as a function of the
invariant mass of the light hadronic state X. If factorization works primarily
due to the large N_c limit then its accuracy is not expected to decrease as the
X invariant mass increases. However, if factorization is mostly a consequence
of perturbative QCD then the corrections should grow with the X invariant mass.
Combining data for hadronic tau decays and semileptonic B decays allows tests
of factorization to be made for a variety of final states. We discuss the
examples of B->D^*\pi^+\pi^-\pi^-\pi^0 and B->D^*\omega\pi^-. The mode
B->D^*\omega\pi^- will allow a precision study of the dependence of the
corrections to factorization on the invariant mass of the light hadronic state.Comment: 7 pages, minor clarifications to tex
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