Sentence examples for quasi distribution from inspiring English sources

These amplitudes relate to quantum mechanical expectations as (langle alpha _{j} rangleapproxlangle a_{j}rangle_{mathrm{QM}}), where (langlecdotrangle) denotes the expectation with respect to the Wigner quasi distribution and (langlecdotrangle_{mathrm{QM}}) a quantum mechanical expectation value.

In the following we show how Eq. (10) and the E ϵ -estimate can be derived in terms of classical and quantum (quasi) distribution functions.

While (10) concerns pure state mean values, our result holds for (quasi) distribution functions which provide these mean values in phase space.

More complicated quasi-distribution functions have been verified recently by means of a double loop interferometer.

In our approach, the generatorAof a quasi-distribution semigroup may not be densely defined.

A proper description can be obtained by means of Wigner quasi-distribution functions which are common in quantum optics.

First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function.

WhenAis densely defined, a quasi-distribution semigroup reduces to a distribution semigroup in the sense of Lions.

We introduce the concept of quasi-distribution semigroups onX, as a generalization of the concept of distribution semigroups introduced by Lions in [19].

For fixedr>0,k∈N∪{0}, define order (r, k) for a quasi-distribution semigroup and define an Fr, kfunctional calculus.

We prove thatAgenerates a (k+1 -times integrated semigroup of exponential typerwith local Lipschitz continuity if and only ifAgenerates a quasi-distribution semigroup of order (r, k+1 -timesonly integratedFr, kfunctional calculusemigroup