Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Quasi-perfect state transfer in a bosonic dissipative network

In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbour resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides an easily manipulated formula enabling perfect state transfer in the special case where the network nonidealities are disregarded. We also extend such a criterion to dissipative networks where the fidelity of the transferred state decreases due to the loss mechanisms. To circumvent almost completely the adverse effect of decoherence, we propose a protocol to achieve quasi-perfect state transfer in nonideal networks. By adjusting the common frequency of the sender and the receiver oscillators to be out of resonance with that of the transmitters, we demonstrate that the sender`s state tunnels to the receiver oscillator by virtually exciting the nonideal transmitter chain. This virtual process makes negligible the decay rate associated with the transmitter line at the expense of delaying the time interval for the state transfer process. Apart from our analytical results, numerical computations are presented to illustrate our protocol.

Estimation or simulation? That is the question

The issue of smoothing in kriging has been addressed either by estimation or simulation. The solution via estimation calls for postprocessing kriging estimates in order to correct the smoothing effect. Stochastic simulation provides equiprobable images presenting no smoothing and reproducing the covariance model. Consequently, these images reproduce both the sample histogram and the sample semivariogram. However, there is still a problem, which is the lack of local accuracy of simulated images. In this paper, a postprocessing algorithm for correcting the smoothing effect of ordinary kriging estimates is compared with sequential Gaussian simulation realizations. Based on samples drawn from exhaustive data sets, the postprocessing algorithm is shown to be superior to any individual simulation realization yet, at the expense of providing one deterministic estimate of the random function.