Non Unitary Random Walks
Philippe Jacquet
Abstract
Motivated by the recent refutation of information loss paradox in
black hole by Hawking, we investigate the new concept of non
unitary random walks. In a non unitary random walk, we consider
that the state s0, called the black
hole, has a probability weight that decays exponentially in
e-λt for some
λ>0. This decaying probabilities affect the
probability weight of the other states, so that the the apparent
transition probabilities are affected by a repulsion factor that
depends on the factors λ and black hole lifetime
t. If λ is large enough, then the
resulting transition probabilities correspond to a neutral random
walk. We generalize to non unitary gravitational walks where
the transition probabilities are function of the distance to the black
hole. We show the surprising result that the black hole remains
attractive below a certain distance and becomes repulsive with an
exactly reversed random walk beyond this distance. This effect has
interesting analogy with the so-called dark energy effect in
astrophysics.
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